Can you tell us more about what we're seeing? (apologies in advance if I make errors in terminology)
It looks like a target reticle about the unidentified object, is that correct? And is it true that the flir is tracking the object in these videos?
It's not a sensor target (which would be used for a weapons lock and come from either a laser or radar). In both videos you're seeing the FLIR doing passive targeting, where the system is trying to follow the contrasting pixels that the pilot has targeted against the background. In the second video that's why it keeps dropping target as he switches through the different video modes - the algorithm for doing this type of tracking changes as you change from IR to TV. Also in the second video you can see that he tried to do range finding with his doppler (sends out radar pulses and counts the time to get a return for ranging - same principle as a police officers radar gun), but the system was spitting out garbage (all 9s) because it was unable to lock properly.
You can tell when the FLIR is moving by the number at the top. The number at the top (which is followed by a degree symbol and then L or R) is telling you which way the FLIR is pointing. 0 degrees corresponds to straight ahead, 90 R would be directly to the right, etc. The FLIR camera sits in a little pod under one of the wings usually, it has a motor that allows for 360 degree turning and a certain amount of up/down tracking as well. Most of the FLIRs that I worked on were for helicopter S&R missions, and our test videos were of pilots flying a few thousand feet above a field and targeting rabbits with the sensors. The F18 ones are slightly different, but seem to follow mostly the same principles.
I know the object seems to be stationary with respect to the imager in that last video, but on your earlier video it looked like the object was moving around the flir which was following it.
Yes, in the first video the pilot is banking to follow the object and the flir is holding on the contrast image to track the object.
That horizontal line above the reticle, does that show the horizon?
Yes.
Would you normally see an exhaust plume in the imagery? Both for a jet engine and a propeller engine?
Yep. The FLIR are incredibly sensitive to heat differences. They can spot the head signature of a rabbit in a field from thousands of feet away, an exhaust plume is very easily visible.
A jet gives a very bright signal from the exhaust, especially when moving quickly. Looks like this in IR:
Even in the regular black and white TV image you can usually see the exhaust when they're pushing the throttle because it's so bright that it contrasts with the dark sky. (In the picture above you're seeing the whole jet showing up as bright because of heat from friction of moving through the air.)
Propeller engines (or rotors on helicopters) won't push out heat like a jet in a plume at the back. The rotors/propellers themselves will usually heat up, and there are usually very strong heat signatures from the motors that spin them. I doubt the object in the gimbal video could have been a helicopter based on the way it rotated in place at the end. Helicopters move in a very predictable pattern, they have to push their nose down in a very particular pattern to get forward thrust from the rotors. Helicopters (and propeller based drones) are very slow compared to jets. There's no way that either could have outrun F18s attempting to track them.