I've known at least two women with red hair who were themselves active ticklers -- a classmate who tickled anybody she could get her hands on, including me, and a coworker who was enough of a tickler to find out that I was ticklish, and then made me her frequent target.
The one time I tried to tickle the classmate back, she squirmed obligingly and threw her head back with a smile, but it seemed like a polite gesture -- she certainly didn't manifest the convulsive movements or uncontrollable noisemaking that plague those of us among the truly ticklish community.
The coworker told a story once -- before she found out I was ticklish -- about how last night her husband started tickling her and wouldn't stop and she got freaked out by how defenseless she was, unnerved by her inability to do anything to make him stop. And added that it was weird because she usually wasn't very ticklish. Once she'd made me her tickle target we were standing in a group in the office and she said something like "Well, and we know Wade's ticklish" and scribbled fingers at my sides making me twitch and giggle. So I retaliated and she resisted, stone-faced -- "Nope, I'm not ticklish," she said -- until I kept it up and an involuntary smile tugged at the corners of her mouth and she twisted away, saying "But I mean it gets annoying after a while."
TL;dr -- marginal ticklishness for those two redheaded women, but that by no mean constitutes a significant sample size.
Digression: I can actually still remember the distinctive feel in each case of their long, pale fingers and sparsely freckled hands -- the classmate, for being such a total tickle monster, was actually not that effective a tickler, her fingers too rough and pincery in their assaults -- but if you were ticklish enough it ultimately had the desired effect (and spoiler alert, I was ticklish enough). The coworker, though was clearly less of a tickling aficionado, was vastly more effective in her scribbly attacks -- every time her fingertips crawled unexpectedly across my sides I couldn't help but writhe and yelp exactly as she intended.