TimFoust:
So If I took a EEPROM reader/writer, I could look at the bit code. If I could do that though, I could reprogram the signs output, right?
You propose to read the EPROM, assuming it contains 6502 code plus character set data and it is still good (looks like the tape fell of), disassemble than and try to figure this beast out? If you are smart enough and have enough time you may be able to do it but I think the number of hours is going to be greater than desoldering reusable parts from this and rebuilding it yourself.
I'm not sure why I would care so greatly how something was witten way back when for a 6502 unless it was a classic video game or something like that.