Alker is aiming for his second major win in the 50-plus rankings. He won the Kitchen Aid Senior PGA Championship last year.
Scotland's Grieg Hutcheon, 68, moved one more step up to third place.
Stephen Alker (c) AFP FILE PHOTO
Overnight leader Jimenez shot a 5-under 66 in the opening round but fell to a tie for eighth place in eighth place after shooting a 5-over 76 including four bogeys between 13th and 17th. Jimenez was the first Spaniard to win the event in 2018.
Bernhard Langer, who last won the senior British Open at Royal Portcaul in 2017, finished eighth with 69 points. He won this major four times and finished second three times.
Defending champion Darren Clarke (74) is five overs.
The tournament is the last of the five majors in the senior schedule. The winner will participate in next year's British Open at Royal Trune.