To answer your question, the shift solenoids are in the transmission valve body. Drop the transmission pan and remove the screen. They are not that hard to access except for the hard-to-access transmission pan screw that sometimes breaks if exposed to salt and corrosion.

Important: are P0753 and P0758 the only codes in the ECM?
P0753 and P0758 are electrical circuit malfunction codes determined by the ECM. I recommend getting access to the factory manual (FSM) for troubleshooting. The factory service manual has the procedures to diagnose the problem.
If you look up the generic OBD2 codes, some sites identify possible causes including low fluid level and fluid condition. However, the FSM lists these fault codes as electrical. The 2001 Toyota codes do not always align exactly with the generic codes.
There are separate codes P0750 and P0755 which are set when the ECM detects that the ratio of input to output shaft speeds is not correct for the requested gear. Having these codes too would change the troubleshooting. They are more likely caused by fluid condition.

With that said, It is always good to check transmission fluid level. There are enough mistakes in the manuals that it is possible that fluid condition can cause these codes without it being documented.
Checking when cold will generally prevent driving with insufficient fluid, but transmission fluid level should be checked at normal operating temperature - about 10 miles of driving. If your scanner reads live data, then the ATF should be between 70 and 80 Celcius. Check at idle speed in PARK with the brake on.
If the transmission fluid has not been replaced in a while, then the solenoids might be a little sticky. I would do a drain-and-fill with Lubegard Red used as directed. You are not out much to try it even if you drop the pan later, since it will take 3 or 4 drain-and-fills to adequately replenish the fluid.

Since you have two circuit codes, I would check the ECM voltage and ground, battery cables, and solenoid resistance. It is fairly easy to access the valve body harness connector on the front of the transmission. I would check the harness continuity before removing the solenoids.

The factory service manuals are available from Toyota TIS, AlldataDIY, and Mitchel1DIY for a subscription. There is a CD version of the manuals on RockAuto, and paper manuals are available from EBay and Faxon. And of course the pirated versions on EBay.
The 2001-2003 are generally very similar, but then very different from the 2004 to 2007.

 

Thanks @C R ! TBH I kind of have no idea what you said but I do know someone at work who does which is a good thing. Also I went to a mechanic and he said changing the transmission fluid on an old car like this can ruin the whole transmission. Is this true?

 

First, at this point, unless the fluid is low, I don't think fluid is your problem.
How many miles are on the car?

I think I can translate what the mechanic was saying:
“I do not want to work on your old car. I can fill my bays and make more money with less risk of a come-back call by doing regular maintenance on newer cars that don’t need diagnostics. If your old, worn transmission fails after I work on it, you will come after me to repair it which would cost me a lot of money”

As with most myths, the idea that changing transmission fluid will cause failure is grounded in truth.
Here is the problem with changing fluid on a transmission that has never been serviced:
If the transmission is worn out, the suspended friction material in the dirty fluid may be helping the clutches to hold. Removing the suspended material may be enough to cause the clutches to slip, which will lead to rapid failure.
Usually a shop will recommend a "professional" flush because it is faster than multiple drain-and-fills, but the concern is that it may also force contaminants into small gaps, particularly the solenoids valves, and cause issues. Also, if a transmission flush chemical was used then it may not be completely cleaned out and would contaminate the new fluid.
There is also the side problem of failing to add the correct amount of the correct fluid, which can cause failure.
Finally, people tend to bring their transmissions in for service AFTER they start noticing problems and the transmission is already failing. The transmission fails soon after service, and so the service is blamed for the failure.
I can't recall any transmission failures being attributed to a service on this forum. Most members find the transmissions to be robust.
A transmission shop or good diagnostic shop can put pressure gauges on the transmission and check the pressures required to hold the gears. This gives good insight into how close the transmission is to end of life. ALL transmissions have brakes and clutches that will wear out and eventually fail, but many of the Toyota "U" series transmissions in the Highlanders have gone over 200K and even over 300K.

What would I do?
There is always risk with any attempted repair. As stated above, it is possible that replacing the fluid could result in transmission failure, but not replacing it can also result in transmission failure at some point.
Wisdom I received from a pro:
If the transmission fluid smells burnt, the transmission is already worn out and at end of life. Do not change the fluid. Maybe try a Lucas product to get a few more miles out if it.
If the transmission fluid is dirty, but does not smell burnt, and the transmission is working well, then it is OK to replenish the fluid and the filter with a drain-and-fill. Use a recommended fluid, and add Lubegard Red as directed (not for all transmissions).
After replacing the fluid, reset the ECM if the transmission was shifting hard or flaring. On our HL's the can be done by removing the negative battery terminal for about 10 minutes. This is done to reduce the time required for the ECM to adapt the transmission pressures to the new conditions.
Do 2 or 3 more drain and fills with at least 20 miles between to get a total of 3 or 4 drain and fills.
Note the difference in transmission performance after each drain and fill. If it seems like it is shifting hard or flares then do not do more drain and fills at this point. Reset the ECM and drive it for a few drive cycles to see if the ECM adapts to the new conditions. If it recovers, then continue to do drain-and-fills.
If the transmission slips, use a friction modifier such as Lucas.
If the transmission has been serviced regularly, like at least every 60,000 miles depending on use, it is OK to accelerate the fluid change with a professional flush instead of taking the time to do 3 drain and fills. I have just taken to doing a drain-and-fill at each of 3 or 4 consecutive oil changes when it is time to change the transmission fluid. I do 3000 mile oil changes and 30,000 mile transmission fluid changes.
There is also a method to flush out the transmission at idle without the pro equipment by carefully draining fluid from the cooling lines while simultaneously adding in the same amount of new fluid. Ralph Spoilsport wrote it up on this forum, so search for that if interested.

 

No solenoid comes out without removing the valve body, don't believe what you see on YouTube. I learned the hard way.