After a delay of two hours and 20 minutes on Friday morning due to fog, six groups returned to the course on Saturday morning to complete their rounds, including Ames who played the tricky par four 17th, the Road Hole, in twilight.
He parred the 18th to follow his first round of 66 with a second round score of 69 for a nine under par total.
Ames will join Jiménez and American Jeff Sluman in the final group on Saturday at 13:45.
Sluman shares third place with compatriot Kirk Triplett and defending champion Bernhard Langer on eight under par.
Tom Watson is just two strokes off the lead alongside Jarmo Sandelin and Vijay Singh, while 2015 Senior Open Champion Marco Dawson is a stroke further back with Mauricio Molina and Tom Pernice Jnr.
Home favourites Sandy Lyle and Colin Montgomerie are two of eight golfers in a share of 12 place on five under par, including former Ryder Cup Captains Tom Lehman and Paul McGinley. Lyle carded the lowest round of the second day at St Andrews, a six under par 66.
The third round of The Senior Open Presented by Rolex will commence at 09:35.
A total of 72 players successfully made the cut.
|1||JIMÉNEZ, Miguel Ángel||ESP||18||-12|