iPhone unable to connect to Mac

I'm trying to back up a family member's iPhone 7 to either her iMac or the cloud before we activate both our new iPhones, especially as we're switching carriers too.

Plugging her phone into her Mac with her Apple charge cord we keep getting Trust queries repeatedly flash onto both the phone and Mac, but disappear before (in some cases on the desktop immediately after) we can press to Trust.

Other questions I've seen about this, the response doesn't get the problem is the repeated flashing/flickering aspect, just explains the Trust process, but I get that, and successfully did it with my phone on my Mac, where I've backed up several other times. The problem is on her devices, the Trust box doesn't remain long enough to click. It disappears and eventually flickers back, with little tonal clunks each time. It asked her to sign into iTunes, which she did (she doesn't use it and may not ever have backed up before). Thanks!