If it is infrequent access, you can get a 1/4 sheet of plasterboard for $12 and cut it to size with a craft or Stanley knife (there is a trick to neat lines though, look it up on YouTube). 

https://www.bunnings.co.nz/proroc-1195-x-595-x-10mm-plasterboard-handy-panel_p0244412

Less robust than some options but you said the last one did 36 years and this will be way easier if you don't already have the tols.

To prevent fingerprint stains, seal it then paint it with a flat water based enamel. Resene do a flat bathroom and kitchen spacecote that would be perfect.