Roger, LED'S are semiconductors, and as such don't obey the well known Ohm's law for current, voltage and current. Mixing LED and tungsten bulbs means there is an imbalance of resistance and current through the various parts of the circuits. Doesn't point the finger exactly, but could account for the unexpected and mysterious things happening. With a tungsten bulb in the rear light holder, looks as if all the current is going that way as it must have a lower resistance than those parts of the circuit containing a LED. The internal resistance of different brands of LED's is probably not specified, and may not be standard between brands, causing an imbalance of current and voltage, hence differing or absent light emission.
For the masochists out there, Kirchhoff's Law will occupy a quiet afternoon, calculating current at junctions. But whether it works for modern LED's, we need some more expert insight.
RD....A little Aldis signal lamp?
Swarfy.