I just took my new Solo on a Mountain bike ride today and we tried the follow me mode once. The phone does need to be on. As soon as I tried turning the screen off it wouldn't follow any more and it just hovered in place. I also found out that the Solo is following the phone not the controller. But they both need to be close to each other so the wifi link doesn't break. My friend put my phone in his bag and started riding (thin pocket on his back). He went a couple hundred feet and it was following him but then stopped and just hovered in place. I flew it back safely with the controller after that. My guess is as soon as the phone and controller lost connection it stopped the follow me mode.
Overall I'm not to impressed with the follow me mode because of this. Shouldn't it be possible to make separate device that the solo could follow? And in the app have an option to switch it over to follow that device instead of the phone/controller. Having to use the phone/controller to follow is not very practical in most scenarios. I film race trucks at off-road desert races and plan on sitting in the passenger seat in a truck to try it out. But I wasn't even thinking about the antennas.
@erikgraham if you find a good solution for cables and antennas to mount on the top of a truck/car please post about it. I think a magnet mount would work good.