Is this a Digital dash?
If mechanical, and you did not get a response from grounding the sender wire, it would indicate the wire or gauge is at fault..
Check the sender wire back to the instrument bucket with a DVOM, set to OHMS, R X 1, Calibrated 000, It should read "000" from the sender to the bucket, If infinite, it's open and needs repair or replacement.
Next if good, locate the "S" terminal on the gauge, (at the laminate card) jump it to ground, and watch the gauge, If it pegs, the gauge is good, and you may have a bad connection at the laminate card or an open trace.
If it does not move, check the "I" terminal for 12 volts at the gauge laminate card) If missing, check the connection and/or fuse.
If it is good, check the "G" terminal on OHMS (no ignition power on) R X 1, Calibrated to "000", it should read 000, if not, you have a bad ground at the card.
If all are good, your gauge is at fault.
The RPM's may or may not be related, (computer thinking it's at high idle, cold, and telling the transmission to hang in at a higher idle..) so were it I, I'd fix the gauge first..you may not have a secondary problem.