Wow- that is weird indeed. The only thing I can think of is the ignition switch. Have you tried wiggling the key around while waiting for GP light on first try to see if it lights? I am reaching here but was about to tear out the electrical system on the heater blower that would work and then not work. Found the ignition tumbler was worn to the point that it would rest on the dead spot between run and start. If I jiggle the key, the heater blower would work....

Other than being annoying (no Light) sounds like your system is working.