scottish civil registration started later than here in England & Wales but one way would be to look for any siblings that may have married or died after the system was introduced, as i recall it was 1855 , anyway, the records you would find him in are going to be mainly religious ones and so you need to look at what places in Methven or nearabouts he or his family could have been baptised, buried in. there is a tendancy to assume that all records have been transcribed for the internet but this is nothing like the truth, you may have to look nearer to the home village to find sources for Andrew and his family.
There is a part census for Perth done in 1766 whichg is in Perth district archives, it is abit early but you may pick up some earlier generation if they are included.
Have you looked at the 1841 census for perthshire? On sites like ancestry.co.uk you can do blanket searches of the census for any surname and this may turn up the previous generation stil alive in 1841.
Until you have established a family group to search for around 1800 it is going to be frustration just keeping looking for the one person, his name may have been misspelt or omitted from the modertn transcriptions