Welcome !
A first good resouce would be the NLS mapping website :
https://maps.nls.uk/ A map nerd like me can lose hours on there ...
Where you can look through historical maps, side-by-side or overlaid with modern satellite imagery, and see if the adit or any associated workings are on there anywhere.
From a very quick look at the area, it seems to be mostly (if not all) ironstone, fireclay or coal in the area. Please, please be very careful, as the atmosphere in such old mines can be toxic or explosive.
However, I do see that, to the SouthWest of Kilwinning there does seem to have been a mineral railway that ran to the Ladyha' Colliery that went through a tunnel, so it could even be an old tunnel rather than a level.
Look forward to seeing some more details, pics, etc !
Madness takes its toll, please carry exact change