Running the gauntlet (gear lever gaiter/cover assembly)

For the gear lever cover inside the car and near one’s hand, was there any clip or tie at the top to make it slightly snug on the lever shaft to reduce circulation?

For the Mark V there are two specified “Gauntlet Assembly for Gear Lever”, part BD.3041 and BD.3679. For the '46-'48 3 1/2 there are BD.899 and BD.1519 “Gauntlet around Change-Speed Lever”.

Here is the original carpet and shift lever gauntlet from my Mark V. The leather gauntlet is sewn into the carpet.

I don’t see any evidence of there ever being a clip or tie on it.

I know the XK120 people talk about a metal tie clip on there, but I don’t know if that was something that came along later.