I think I figured it out -
The TM501 and 503 are the powered chassis for the AM5xx amplifiers? Is that right?
Exactly, but they're not just for the AM5xx amplifiers! The TM 5xx are Tek's universal power mainframes used from the mid-70's until the late 80's. They produced a few dozen separate instruments for them. Everything from DMMs and power supplies to frequency counters, function generators, amplifiers and even tiny oscilloscopes!
The last digit in the model number of the TM (which I assume stands for Tek Mainframe) series designates how many slots it contains. So a TM 501 is a single slot unit and a TM 506 is a six slot unit.
The various plugin designations have similar names:
AM5xx = AMplifier
PG5xx = Pulse Generator (Square Waves)
SG5xx = Sine Generator
FG5xx = Function Generator
TG5xx = Time Mark Generator
DM5xx = Digital Multimeter
PS5xx = Power Supply
Plus several other types.
They're surprisingly useful mainframes as you can often get the plugins pretty cheap. I just picked up a SG 504 250MHz to 1GHz Leveled Sinewave generator for $100!
Just make sure you don't accidentally buy a TM 5000 series mainframe or plugin, as they're not backwards compatible with the 500 series.
The 500 series mainframes are pretty simple. It's essentially a huge transformer with a few dedicated windings (providing low voltage AC) and (rectified and filtered) 12VDC for each slot on the mainframe along with a high current (rectified and filtered) 32VDC bus shared among all the slots. There's also one NPN and PNP transistor for each slot (bolted to the metal frame for heatsinking).
If you buy a mainframe from eBay, I'd recommend replacing the caps. There's a couple of 5000uF ones plus a big 20,000uF one (if I remember correctly and at least for the three slot unit). Don't try desoldering the wires that go from the board to the transformed; instead just unbolt the transformer and unscrew the board and remove them together. Once out of the mainframe there's plenty of room to easily unsolder the caps. They use those old 4 terminal Sprague caps, however the hole spacing was standard, so you can replace them with your choice of snap-in style caps.