My Rheem forced air heater is old - about 15+ years. It was working fine last week,
But last night the pilot light went out. I can find absolutely no way to re-light it.

You sure it has a pilot light?

Does the furnace have a small blower in the burner compartment that comes on when you turn the furnace on?

At fifteen years old, I'm also guessing you don't have a standing pilot. Can you give us an exact model number of furnace, or a pic of burner area would also be great. Im guessing your rheem has a glow plug(as the older ones did,) If your unit is older than fifteen years old, you may have a rheem imperial, in which case, I say, time to start looking for a new furnace, the imperials, I believe, had intermittant pilot spark ignition. Please let us know a little more about your furnace, and we will do our best to help. Lee.