Air carrier Captain reported an EGT fail on the #1 engine and other erratic engine indications during approach. The flight continued to a single-engine approach and landing; with normal passenger deplanement.

Narrative

Approaching ZZZ; we experienced an EGT FAIL on the #1 engine with erratic engine indications. We notified ATC of Aircraft status; gave soul count of XXX; fuel [remaining]; CFR (crash fire rescue equipment) to meet aircraft upon landing; and our desire to land on longer runway of XXL. Flight Attendants were fully briefed on the situation. QRH pertaining to ENG FAIL complied with. First Officer (FO) maintained control of aircraft while Captain completed all checklists; briefings; and ATC coordination. At approximately 6;500 ft. MSL; all checklists were complete and appropriate data entered. Captain took control of the aircraft; as PF; to perform the single-engine approach and landing. Aircraft landed normally. CFR circled aircraft to ensure all was well. Passengers briefed. Brake cooling module was performed. We waited the required XX minutes for cooling. Aircraft parked at the gate with normal Passenger deplanement. Captain met with ZZZ Maintenance. Captain performed a full Flight Attendant de-briefing. Captain then called the ZZZ1 Chief Pilot on call; Maintenance; Supervisor; and Dispatch. Captain further met with the ZZZ Chief Pilot to complete debriefing. No further incident ensued.