+1 for motorbike
Although I suppose the issue would be that with greater speed you pay less attention to the surroundings. On foot you’d scan every inch of the ditches either side, on a mountainbike you’d keep an eye on them, on a motorbike you’d mostly ignore them as the trail takes all your focus.
There are a few places that an ebike can go where a trials bike cannot due to the weight. You can carry an ebike up a climb where a trails bike cannot go.
A combination of rider skill/fitness, bikes capability and the trail though. If it’s genuinely that steep then why bother with a bike, it’s actually slowing you down looking of the casualty. And I don’t believe you could carry an e-bike up a steeper slope than a trials bike could ride.
Drone with an IR camera seems the much better thing to spend money on though if you don’t know where the casualty is.
Going faster on the ground only really works if you’re looking for someone on a trail and you know where to find them.