Playing on his birthday, Alker made four birdies in the second round along with a bogey at the par-4 10th.
The New Zealander is four-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 further stroke back in third.
Overnight leader Jimenez had an opening-round five-under 66 but dropped down to an eight-way tie for eighth after a five-over 76, including four bogeys between Nos.13-17.
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…