I started by unplugging the speaker and removing the grill cloth, taking pictures of screw placement and bagging the fasteners together in logical groups. The result was easy access to the collected layer of filth. Bleugh.

The amp's proximity to the window seems to have turned the cabinet into a flytrap.

I vacuumed out the cabinet. Much better. Not clean, but stomach-able.

I could then drop the chassis out of the cabinet and see what kind of circuit was in this thing.

Yup. Definitely solid state. The aluminum bracket in the middle is the heat sink for what is obviously the power amplifier chip, an LA4460.

The circuit has no obvious faults, charred components, or broken bits, so it's entirely possible that nothing will need done to the electronics, but confirmation will have to wait for another day. In the meantime, the amp has no obvious branding anywhere on it. The tolex seems to have been amateurishly replaced at some point and stapled haphazardly into place. Presumably when that was done any logo was lost with it.

There are two stickers still covering potential identifying information, though, hopefully a brand is hiding under them.

Nothing hiding under there.

A generic brand speaker. Nothing that can help me find a schematic for the circuit should something be wrong.

Since the circuit looks okay and I can't find any schematic should it not be, I plan on testing the amp before I do any more teardown. If it works, I'll note where all the connections are between the bits of the circuit and disassemble the chassis for cleaning. If it doesn't, I'll create a schematic for the circuit and try to diagnose it.