A few things.

Make sure the bulbs are the exact trade number / wattage as original. Any name brand bulb is fine as long as it is the correct wattage and meets trade design specs. From the systems I've seen that test bulbs when they are on, the module is looking for a specific current flow then decides if the bulbs are working. If current flow is low the warning will light up even if the bulb is lit. They might also look at too high current flow and trip a light.

Any corrosion in connectors / sockets is going to reduce current flow. If you have a failing ground, all sorts if strange behavior will occur also.

If you have a system that tests bulbs without turning them on, I have not researched how they work.

Electronic components start to go off spec. Electrolytic capacitors dry out and fail causing all sorts of odd behavior.

Bulbs wear out before they burn out. The filament starts to loose tungsten and gets progressively thinner, I haven't checked resistance but I'd expect it to go up as the bulb ages. Also, a filament can have a break, the broken strand will flop about and sometimes reattach allowing the bulb to light up again.