A B737's number two engine N1 gauge and EGT gauge alternately indicated full scale high with red lights; but the engine operation remained normal.

Narrative

After leveling at our cruise altitude of 32;000 FT we observed the #2 engine N1 gauge go to full scale high RPM and the red light illuminate. All other engine parameters were normal. The N1 indication did not respond to throttle movement. After approximately 20 seconds the N1 gauge returned to normal. After about 5 minutes the #2 engine EGT gauge did the same thing. Tapping the gauge had the most effect on the indication. After this second occurrence; which we determined was most likely an indication error; we had no further problems with the indications until on final approach. On final approach; once again the EGT gauge went to full scale high and the digital display went blank. I pulled the #2 engine throttle to idle and treated it as a single engine approach and landing. Prior to landing; the #2 EGT returned to normal. Apparently there was a defective system in the #2 engine that reported certain parameters. The aircraft was repaired and returned to service approximately 24 hours later.