Just giving back some information to this very helpful community:
My problem was the vacuum modulator (aka vacuum regulator valve). I replaced it and have been driving trouble-free for a couple months.
I confirm the following key points discussed in the thread
96 corolla with p0401 check engine code
1) What user "kevmac" said about Haynes manual: the testing procedure for checking the vacuum modulator is insufficient. I suspect this test only checks whether it is clogged inside. My modulator passed that test (I blew air into it, and saw air come out the specified ports), but was still defective.
2) What user "msrdude" said about applying vacuum to the bottom port. My old modulator did not hold vacuum, the new one does perfectly. This test checks whether the diaphragm inside the modulator is cracked/broken.
3) What "Dirty Dude" and "JesusJones" replied: there is no EGR gas temperature sensor in the 1.6L engine car.
Once again, many thanks to the people who replied, and who posted their experiences in other threads!