Dolby A can be scary these days.
I have working 361 series models (single channel) and a 363, dual channel (also with Dolby SR).
What is scary?
First of all your tape deck must have balanced XLR line outputs.
The cat. 22 decoder cards in the 361, can develop faults in any one of the 4 frequency bands
that the recording signal has been split into.
(The input signal is split into four frequency bands with 12 dB/oct slopes:
lowpass @ 80 Hz; bandpass 80 Hz - 3 kHz; highpass @ 3 kHz; highpass @ 9 kHz.)
No internal adjustments on the card.
The only fix is to replace with a different working cat.22 board in the unit in question.
How do you test your board?
Why with an unobtanium Dolby NMR test set cat. no. 35 of course!
Perhaps Charlie could chime in on the Dolby since he's worked on and fixed a few in his lifetime.