I found that teardown picture by googling "U151E solenoid"
I got this sonnax ID guide Sonnax - Aftermarket replacement transmission, torque converter, and high performance automotive parts
which specifically mentions "SL1 is a clutch control solenoid and is also known as Pressure Control Solenoid "A"."
Pressure Control Solenoid "A" AND SL1 is what the repair guide for P0746 states.
So, I have the location in a guide from sonnax, and I found the teardown picture with the toyota part numbers from this picture
(by googling U151E solenoid and looking at google images)...
Then I matched the 35210 parts number to toyotapartszone.com
For Toyota parts its called "SOLENOID ASSY, CLUTCH CONTROL, NO.1"
So what is it?
1. Pressure Control Solenoid "A" (repair guide)
2. Shift Solenoid Valve SL1 (repair guide)
3. SL1 (sonnax)
4. SOLENOID ASSY, CLUTCH CONTROL, NO.1 (Toyota parts database)
It's ALL of them... no wonder the parts guys on the phone were VERY confused. I got quoted $480 from one of them... lol...
of course default to charge me the most $ and they can't go wrong ordering any of them
Not at all easy. Now I know what mechanics and parts guys can sometimes go through.