The tournament is played over three courses, Carnoustie, Kingsbarns and St Andrews, with the latter also hosting the final day.
Jarvis shot a 67 at Kingsbarns to back up his 66 at Carnoustie on Thursday to sit at 11 under par.
"It's nice to have the old course for two rounds in a row now," said the South African.
"You watch the (British) Open growing up as a kid and now to be in contention in a tournament like this, I'm just looking forward to it and I can't wait to get out there over the weekend."
England's Matthew Jordan is tied for second place, alongside Spaniard Rocco Repetto Taylor and M.J. Daffue, after beating his previous score at Carnoustie by five shots.
Defending champion Bob MacIntyre shot into contention at eight under after a 65 at Kingsbarns, while five-time major champion Brooks Koepka hit a 67 to also sit three off the lead.
Tommy Fleetwood is at six under after a four-under 68 at Kingsbarns, as is Ryder Cup teammate Matt Fitzpatrick.