Here is a video of a shuttle launch taken at very close range. The shuttle has two solid rocket motors each of which is much bigger than an ICBM motor. At about 1:30 into the video why can't we see any glow from the motors? It "would be constant" right?
Well, it was constant... and it receded quickly downrange... and looks absolutely nothing like that contrail. Especially the downrange part.
Sorry...
30 seconds into launch, over 3 miles altitude. Note the tight exhaust trail.
40 seconds later, rocket has gone 17 miles higher - over 20 miles in altitude. Serious fire from the rockets - no doubt, no dull redish reflection appearing briefly then disappearing.
Solid booster rocket separation:
And finally, three minutes after launch, extreme zoom sees the fire end of the rockets disappearing, traveling over 2,600 miles per hour.