There was a supplementary chapter in Vari plans which has lighting. The plans specify to install strobes on the fuselage rather than piggyback wingtip strobes (piggybacked on the red/green position lights Grimes or Whelen style)
For the upper strobe/position light (white) a Whelen A500 series is specified. This is a combination light with a strobe tube and a halogen bulb. I have tried replacing this halogen with LED and had no luck for durability.
For your lower forward strobe (under pilot seat) I do not remember what the spec was however I have a streamlined Hoskins housing from a Learjet with a Whelen emergency vehicle flasher bulb mounted.
I use a Kuntzelman flasher power supply for 2 strobes. It's a reliable system after about 450 hours.
If you have a no fire situation, Take one tube and hook it to your power supply.. Make sure the connections are good as the original terminals may be burned. If you don't hear a whine noise from the pack then it is likely dead. If you hear a high pitched whine try pulling and swapping tubes. If no flash then it's again probably your power pack and this time it's likely really dead. If no whine, and you're halfway competent at electronics, open up the case and check the soldered on board fuse... good luck