That's a reasonable assumption you've made, but the lamps are run from a separate tapping on the transformer, rectifier and filter caps.
Your loud big bass notes are causing a big surge of current from the transformer secondary and in turn a big flow of current from the primary side. That drop in flux density causes the separate windings that your bulbs are connected to, to have a momentary drop in secondary voltage. As the bulbs are all in series any small voltage drop will be manifested as a visual fluctuation. There are 470uF 50v capacitors across the rails (+/-36v) and increasing their value would make a change for short duration transients- you could safely increase those caps to 2200uF and other benefits would flow from that as the regulated front end and preamp is also run from that supply.
Your main caps essentially just supply current for the power amp stage when the transformer isn't.