Bluetooth Keyboard Battery Level Sensor Inaccurate

Late 2012 21.5" iMac OS X El Capitan

Wireless keyboard battery level is always at 100% (all places where level is stored: system preferences, system report, Bluetooth icon on menu bar) regardless of actual battery strength even if close to 0%. Wireless trackpad battery level is normal and both wireless devices operate well and with a fairly long time between necessary battery changes. Worked fine when system was first purchased but has not worked for a year or so and has not been helped by OS X upgrades. Apple hardware test indicates no faults.

Have unpaired and paired device, got a new wireless keyboard, reset SMC, started in Safe mode, and tried other procedures to fix the issue.

Any ideas would be very much appreciated.