Funny.....just last night I was going through an Asteroids Deluxe board with a friend...had a constantly beeping board as well.......it was a bad/dirty PROM socket (where the two are typically socketed in row 2 - forgot the locations?) and both TLO82's were bad...fired right up and played perfect after that. So maybe we are discovering a more common failure mode out there. Just last week...the same friend had two bad sockets on those same PROM's (Tempest board this time).....and the funny thing is....once those are going wonky you start seeing random RAM failures with the low/high tones. When I see that...I always go back to those 2 PROM's and sockets. The other symtom I noticed when the two PROM's/sockets are bad are the player 1 & 2 lights staying on when you power up...along with the constant beeping or continual beep. Once those lights extinguish and the slam switch is showing signs of life in test mode....you know you are getting somewhere.
I 100% agree....going into the vector generator circuits with a probe and comparator usually results in a headache for me as well....