As Englishman Paul Waring stayed out in front after following his opening 63 with a 70 to sit on 11-under, Forrest kept him in his sights with a 69 to lie just two behind in a share of second spot.
“We had weather like this at Open Qualifying a few weeks ago which is not what you want when you have two holes left,” said Forrest of having to battle torrential rain at the finish on the Lancashire coast.
“I ended up hitting 2-iron, 4-iron into the last which would normally be 2-iron, with a 9 or 8-iron maybe, so it definitely made it a lot tougher in the end.”
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The Hero Open champion - he defends that title at Fairmont St Andrews next week - signed for five birdies and two bogeys.
“I didn’t quite play as well as yesterday, a couple of loose tee shots, but I dug in well and made a couple putts at the right time and just managed to keep the momentum going,” he added.
“Golf is such a fickle game, I feel like I have sort of found something in the swing, and I have been working hard, just trying to stay patient and wait for things to come good and hopefully this is the week. The whole game feels quite tidy at the moment.”
Richie Ramsay shot a second successive 69 to sit in tie for eight on six-under, four ahead of Bob MacIntyre, who was in danger of missing the cut after running up a 7 at the 17th - his ninth - but then came home in three-under.
David Drysdale sits on one-under after a 72, with Craig Howie just scraping through on level-par after he followed a 67 on Thursday with a 77.
Elsewhere, Gemma Dryburgh made the cut in the Amundi Evian Championship, the penultimate women’s major of the season, on one-under after rounds of 71-70 in France, where Canadian Brooke Henderson (64-64) leads by two shots on 14-under.