Center Controller reported a small aircraft experienced an electrical failure and lost communications. The aircraft safely diverted to a nearby airport.

Narrative

Aircraft X checked in level 040 enroute to ZZZ. Later; Aircraft X tried to contact me. I responded but received no further transmissions from Aircraft X. Lost the aircraft's Mode C and provided the altimeter again. I repeatedly tried to re-establish communications by switching to standby and BUEC (Backup Emergency Communications) transmitters. Aircraft started turning right-of-course and squawked. I acknowledged the squawk in case they could still hear me and could not transmit. I assumed the aircraft's engine went out or electrical issue. ZZZ1 airport was the nearest airport and they appeared to be heading toward it. I called out the position of the airport. I used another aircraft to attempt a relay to the aircraft to find out what the nature of the emergency was.I had the aircraft go to ZZZ1 CTAF as well. All relay attempts were unsuccessful. Radar contact was lost about 4 minutes after this started. I copied the LAT/LONG and gave it to the Supervisor. I solicited an ELT report from a high altitude aircraft; which was negative. I was able to see a primary target tracking toward ZZZ1. At this point; I thought it was more likely to be an alternator failure. I had another aircraft switch to CTAF frequency and try to turn on the runway lights. They were 30 NM west at 080 and unable to confirm if the lights had been turned on. A few minutes went by and got word from the Supervisor a Sheriff's Deputy had located the airplane and pilot safely on the ground at ZZZ1. I would have liked the ability to transmit on the CTAF frequency to turn on the airport lighting and/or attempt to communicate with the aircraft. If I had the pilot's phone number; we could have called them on the telephone. In a dream world; secondary ground to air communications should be like joining a conference call using mobile phones on the aircraft.