Originally Posted by Glock
Would the heating element touching the inside of the RIMS tube cause the GFCI to trip?
No. Water is conductive so having water touch the heating element would have the same affect as the element touching the side of the tube.
You really need to buy yourself a multimeter if you don't already own one. Use it to measure the resistance between the different wires. You should measure 10-20 Ohms between hot and neutral. You should measure an open between either of them and ground. Sounds like you have a short between one of them and ground. Start disassembling the RIMS tube to see what's causing the short.
You should always use a multimeter to ohms things out before you plug anything in.