Your best bet is to obtain a copy (library) of the relevant AK Hamilton Jenkin, "Mines and Miners of Cornwall". I think it's Vol 8 "Truro to the Clay District". In the back of that will be a map and you will be able to see quite clearly what the closest mines were. I think Parka Mine was aka Toldish Tin Mine (they often had several names....there was also a Toldish Iron mine as well.
Armed with this knowledge, go on google and type in CROCAT Cornwall and it will give you the record office search page. Whack in the names of the different mines and off you go.
Failing that, Cornwall Studies Library at Redruth (which is amazing) has some very helpful staff and a huge amount of information. I would get in contact with them first as the CRO probably has enough information in that immediate area to keep you busy for several weeks. 1860 is the sort of time when lots of records were kept.
Good luck. Stu