I may need to replace the furnace; I really don't know why because it's 'only' 21 years old. Anyway, it's always worked fine but on this trip, it only lights when electricity is available. Unplugged...
Furnace is strictly DC (unless you have an AC style)
IF it fires up and heats while connected to an AC power source but doesn't w/o AC power than the DC voltage from batteries is low or at issue.
Check DC voltage at furnace while on AC and w/o AC.
Dirty/loose/corroded connections/contacts cause resistance. Doesn't take much resistance to stop DC power. The lower the DC voltage the easier for any resistance to impede.
Good cleaning of contacts at furnace may solve your DC issue