Have you tested the charging system? 1200s have a reputation of the stator (alternator) going bad but it may just be burned up connections. Remove the battery cover and to the left of the battery there is a connector with 3 yellow wires, it tends to melt and loose connection. The best fix is to cut out the connector and solder the wires solidly together. Also there is the connector at the voltage regulator that tend to do the same but not as bad.
The 4 cylinder wings have small alternators and the 1200 seems to have a reputation of a weak charge system . Pull off the battery cover and look for a wire plug connector beside the battery . It should have 3 yellow wires . It is very common for this wire connector plug to fail . It may actually be melted . The comon cure for this problem ,( should it be the problem in your case ) is to cut the connector out of the harness . Slip some heat shrink tub over the wire , solder the wire connections and then shrink the new insulation tube in place . There is no worry about which wire goes where . Just put a yellow from the engine/alternator harness to the upper harness yellow wire . Once you have done all 3 wires with soldered connections you should be ok unless your windings have failed . . Here is a link to a testing procedure:Bikers Workshop Series If I remember correctly your alt output is just around 300 watts . If you add to much lamp load it will run the battery down .
Do yourself a favor and disconnect the plug andhave a look at both halves. Then just for piece of mind you should still cut out the connector and solder/heatshrink.
The 1200's aren't known for thier robust electrics. We have to get by with our GOOD LOOKS. After starting the engine, a 30 minute ride with a lot of extra lights might not be getting the battery fully charged. Might not be a bad idea to have the battery load tested either. Could be one or nore cells getting tired... :gunhead: