Well. I wonder how many folks here have ever used a model 28 Teletype (NO Lower case, you need at least a model 33 before you get lower case).
Question: Do the lights SLOWLY Dim or rapidely DIM.
SLOWLY you may have a bad charger section in your inverter (or converter if you do not have an inverter) or you are drawing so much power it simply can not keep up (not likely. My Inverter can kick 100 Amps).
So i'd start with the inverter
If the lights SUDDENLY dim. a circuit breaker between Inverter and battery.
NOTE: I seriously doubt that one.