I had a similar problem but doubt it's related on my old FH. I got no sound when I turned it on but did in test just like you. If turned off and right back on it would be fine. I thought maybe a cap was going as it was draining and off and on was recharging it but I was way off.
It ended up being my PDB (As I sent the board out as I screwed up and wired in a flipper coil wrong and friend a transistor - they updated the board while in there, etc.) but not noticeable at first. I did a PF swap and came to be after that so I figured I had to have caused it. I ended up sending the board to the same repair place and they found some bad caps to replace, replaced the amp, updated sound ROM's, reflowed headers and checked fuses. Thought I was set and it still did it. Another local tech was able to figure it out the issue- Thanks Ryan! I don't do board work so I wish I could explain more but it wasn't what I would've thought.
Long story short, check your voltages and make sure that's ok.