LEDs are diodes, therefore they only conduct in one direction. If you hook them up backwards, they won't be damaged, they simply won't light. It MAY be possible, but doubtful, that some LED replacement lamps have internal bridge rectifiers which will allow them to operate on either polarity, or even AC
If you want to check out the gauges (excellent time) you need to get a wiring diagram so you can figure out which terminals go where. What year/ model/ dash do you have?
Go down to Radio shack and buy some resistors to check the gauges. If you do nothing else, buy 4 - 100 ohm, 1/2 watt resistors, and put all 4 in parallel, for 25 ohms. When you substitute that resistance for the sender, the gauge should give you a 1/2 scale reading.
The test resistances are:
L = 73.7 Ohms (empty)
M = 23.0 Ohms (1/2)
H = 10.2 Ohms (full)
My 67 had several problems with the PC board, and you should go clear over it, or consider a repop board
On mine, several of the connector pins were loose/ corroded, and broken clear off.
The board was dirty and corroded, so clean them around the lamp sockets
The brass spring contacts where the gauge limiter plugs in were not making contact with the board. I had to solder jumpers across from them to the board
The VR itself was bad
The nuts on the gauges were not making contact with the board. Loosen/ tighten the nuts, or replace with "real" nuts
Consider replacing the VR with a good aftermarket solid state one.
