The long and short of it is the reverse polarity light can only be caused by a few things,
1. hot, (AC) on either neutral or ground - You hooked up something wrong, or the heater has an internal short.
2. Open neutral - corroded connection, or you hooked up something wrong.
3. Open Ground - either the furnace is not correctly grounded to the inverter, or the inverter is not correctly grounded., or you hooked up something wrong.
If you are blowing fuses
, you need to take a big step back, and pull out a voltmeter, and double check ALL connections.
If grounding the neutral, ... ANYWHERE, blows a fuse, (neutral should be at ground potential anyway, remember?), You have hot on the neutral, which is exactly what the light is warning you of.
Abraded wire insulation
, check where it goes through panels
, (you used electricians nipples, right? They have a plastic inner liner to prevent chafing).
Check with inverter manufacturer. Most houses are wired for 208V - split phase, the neutral is the phase splitter, and tied to ground at the main panel. You use the outside lines for 208, and 1 phase to neutral for 120Volts.
Most inverters are 120VAC, 1 phase, NO NUETRAL. Both outputs are 1/2 of the 120VAC. One of them is arbitrarly picked to be the "neutral" by the inverter manufacturer, and grounded in the inverter.
As the inverter uses the incoming AC to "sync" the AC output you should follow their recommendations on where and how the neutral is connected and whether it should be grounded before or after the inverter.
on a boat and a house are very different. If this is a house installation
forum would be better consulted.
I am curious about the wattage of the furnace, and the inverter, as most house electric furnaces are 10KW or better, and 208VAC.
A common failure of house furnaces are debris, or insect landing between elements and supports causing a resistive short to ground, or the wire in the element can break or deform and bridge to the frame. If the short is near the end of the element the furnace will continue to work, but the frame will be slightly "hot". The short can also make and break as the element heats up and expands.
If the furnace is connected to a typical house utility power you will never notice it unless you actually go into the attic and touch the frame of the furnace with a meter, (unless you by some chance use a ground fault breaker on the furnace, "not likely").
BUT if the furnace is powered by a local source like an inverter, this current
leakage can cause detectable problems, (My inverter has built in ground fault detection).
The above advice about hiring a professional should not be lightly ignored. Electrical
looks easy, but wiring regs have been developed by years of experience by engineers with a great deal of knowledge of the fundamental properties of electricity.