1959 series 62 restoration step 15

[J.Pegler]

First a bit of background, 1987 at the age of 15 I purchased my first car the 1959 Cadillac series 62 2 door hardtop for $2500. This is a California car and could realistically just keep going as is however, I have earnestly begun the restoration I've been imagining for the past 36 years. I'm at a place in life now where I can really make this happen. I've restored numerous cars over these past decades and I have refined my skills and processes to the point that finally this caddy will get my very best knowledge and patience to really do this correctly.
So today I have a simple question for the forum about my shifter handle and turn signal selector handle. The resin type interstitial detail has shrunk, crazed and worn away. I would like advice or the true answer of how to dismantle the stack of parts that are attached to each handle.
The chrome cap does slightly twist on the main shaft, but does not really give me the feeling it unscrews. Press fit? Some kind of cement in there? Does it need heat?
Before I go and apply serious force I want to query this group for knowledge of how I should proceeded. See pictures below.

[Moody]

The chrome end and painted part are reproduced. And yes, it's a press fit.

[V63]

I am sewing up an interior for one of these now. Yikes ! All those seat pleats are a challenge!