I have this old fluorescent desk lamp from the 60s at the latest that I'm fixing. It weighs a ton, has been passed down from my father-in-law, and it just retro-cool. According to him it's always worked, except the F15-T8 bulbs are possibly original and very worn out, and only one bulb ever lights. I've been told this has always been a problem, and holding the start button for a long time will sometimes get both to start. I've never been successful but I don't like this and want to fix it.

Upon reverse engineering it I come up with this schematic (it's rough, drawn in Paint!):


https://imgur.com/a/0YYKV

I'm no fluorescent light expert, but how the start button is connected to both lamps seems odd to me, a little like directly paralleling LEDs or neon bulbs after the limit resistor. If I disconnect one bulb, the remaining always starts. I doubt this design would ever work very well....would it?

If I manually start each light by disconnecting the start button wires and momentarily shorting the two pins at opposite ends of each lamp, they each start right up. My plan is to modify it with a DPDT relay with 120VAC coil so the start button drives the coil, and each lamp has it's own set of relay contacts. I'm sure this will work, but.....WTF with the original design? Is this normal? I doubt it's even been modified, and see no good way to fix it without adding a relay or a multipole start switch.

I'm a little surprised to see some that seems this hokey (to me) in something this old.