It looks like that relay gets pulled closed by grounding pin 1 on the JL901A connector, and that signal is probably coming from the main board in response to the signal on pin 5 of the same connector (STPOWER). From what I can tell, the PSU is always supplying the 9v and 12v rails even in standby, and trips that relay when it comes out of standby. So, if there is no signal on STPOWER or POWERD, then the relay isn't closed. If you are trying to test outside of the chassis, trying bridging pins 3 (GND) and 5, and see if it stays live then.
If something failed in that signal train, I would start looking at the transistors at Q9005 and Q9003. Also, check to see if you have +9v and +12v on Pins 2 and 4 respectively (vs gnd on 3) on that JL901A connector. I'm pretty sure that the relay only controls power to the amplifier transformer T901 on the other end of P9002.
To be clear, the signal for that relay comes from off the board. Jumping it shouldn't do anything when it's isolated from the rest of the system. I don't know what's happening on the other end of the mainboard connector, but it looks like the behavior is:
Mains attached: Some signal on STPOWER pin 5 (I'm not good enough to do the math to figure out if it is anything from 12v down to 3.3v logic level), +12v on 4, GND on 3, +9v on 2, and 1 floating unconnected, 12v when connected and in standby, GND when on.
On the relay, you should see 12v on pin3 and pin2 should be floating. If you ground pin2 on the relay or pin 1 on the connector, the relay should close.
Fixed! Edited the OP in case you're interested.
Wow, you put a lot of work into helping me. Thank you so much! I edited the OP to include the main board, mainly for posterity, in case someone else needs it.
I'll tinker some more tomorrow or next week if I remember to bring my portable scope. (I didn't this morning) When I hooked the standby power supply up this morning and this time connected it to ground, it worked briefly but quit again, just as I tried to show the guy that owns the receiver.
I'll keep you in the loop.
It's not that much work, once you start to get the feel for a schematic. I really don't know how to make power supplies, but I've seen enough arcade and radio repairs to know how to start tracking down power rails, which is 99% of "it's broke" problems.