Playing on his birthday, Alker hit four birdies in the second round along with a bogey at the par-4 10th. The New Zealander is 4 under overall and leads his fellow 52-year-old Alex Cejka (71) of Germany by a shot at Royal Porthcawl.
Alker is chasing his second major victory in the over-50 ranks. He won the KitchenAid Senior PGA Championship last year.
Scotland’s Greig Hutcheon (68) is a another stroke back in third.
Overnight leader Jimenez had an opening-round 5-under 66 but dropped down to an eight-way tie for eighth after a 5-over 76, including four bogeys between Nos. 13 to 17. Jimenez was the first Spaniard to win the tournament in 2018. Bernhard Langer, who won the last time the Senior Open was held at Royal Porthcawl in 2017, carded a 69 to also share eighth. He is a four-time winner of this major and has been runner-up three times.
Defending champion Darren Clarke (74) is 5 over.
The tournament is the last of five majors on the senior schedule. The winner gets into The Open next year at Royal Troon.