Found some old Zenith tube radio...

[mr_rye89]

I have an early 60s plastic Zenith AM/FM clock radio that has a very similar chassis to yours, the main difference is mine has a silicon rectifier and all the coupling capacitors in it are ceramic disc types. I did see the one wax/paper capacitor on the back, so likely there's more inside. Those wax/paper caps should be considered bad at this point and should be replaced.

My Zenith was working as found, despite the original filter caps. It seems like I had to clean the power switch on it once though.

These sets are transformerless and a bit dangerous if you don't know what you're doing, as the chassis can become "hot" if it's plugged in backwards. And if it has a selenium rectifier that should be considered bad too. You might have to get the chassis out of the box to access it though