Slim to none! Just pay your 50p at Falkirk Grahamston and be done with it. Don't even think about using Linlithgow (although there is a newish overflow carpark round by the cricket field that does not always fill up - NB it takes longer to drive there than to walk from the station & this is on the Edinburgh side of Linlithgow so more of a drive from your direction [if you go under the canal bridge you have gone too far!]).
Uphall carpark is busy too but does not generally fill up completely. It is a bit of a slitter to drive there from Falkirk (take the former A9 now A803/B9080 to Threemiletown*; right onto B8096 through Ecclesmachan to Uphall; right at lights then left at mini roundabout again B8096 - watch for speed bumps as I lost my exhaust there; then straight on across the A89 junction to Uphall Station) - to be fair if you have driven that far you may as well carry on to Edinburgh.
I park at Polmont, Linlithgow, Uphall, & Dalmeny depending on my shifts. Parking at any of these stations is a nightmare between about 08:00 - 14:00
. Good luck!
It's nothing to do with paying 50p......inconveniently there is 0954 from FKG to EDB with the next one being 1024 - this is the first R/C eligible one but gets me in to late.
The 0954 ex FKG stops at Polmont at 1000 hence ok for travel.
Is parking 50p at High as I note there is a 1003 departure from there that would be ok.