WE have long known about this entry in The surnames of Scotland by George Fraser Black:
James Thrift was reidare at Culles (Collace), 1574 (RMR.), and Mr. James Thrift was reader at Auchtooll, 1671 (Edin.App.).
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In searching for more about these James Thrifts I found the following, which can be found by searching for "sir james thrift"
Ancient criminal trials in Scotland: comp. from the ..., Volume 1, Part 1
By Robert Pitcairn, Scotland. High Court of Justiciary

page 334
1547
Treasonable Fire-Raising -- Stouthreif &c
May 31 James Gall, Thomas Thrift, and Sir James Thrift, Chaplain, found caution (Archibald Douglas of Kilspindie) to underly the law, at the next Aire of Perth, for treasonable Fire-raising, and Burning the houses and dwelling-place of Alexander Skrymgeour of Balbegys: And for Burning Jonet his daughter: And for Stouthreif of his Title-deeds and goods &c.
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This seems to be a different person from the above:
James Thrift, skinner, and/or his wife Janet Kyle interred 7 Oct 1693, west kirk, Greyfriars buryingground, Edinburgh

Peebles is ~15 miles south of Edinburgh, across the Firth from Kirkcaldy
The following probably has many typos introduced by archive.org as well as the original creative spelling:
EXTRACTS FROM THE RECORDS OF THE BURGH OF PEEBLES
8 April, 1689.
Mutilation of James Thrift, skinner, burges of Peebles, being accused for ryveing of ane leaf out of the toun court book, quhairin wes written ane act of caution, granted be him as principall, and Adam Lytle as cautioner, that John Govan, proveist of Peebles (who hes deponed that he did dread the said James Thrift bodily harme and oppressione) his wyf, barnes, and family should be harmles and skaithles in thair bodyes, goodes and gear, and should be nowayes troubled or molested thairin be him or any he may stop or lett, othervvayes then be order of law and justice ; compeiring, personally confest the lacerating the said leaf out of the forsaid book, and comes in the counsells will thairfor.
(Signed) James Thrift.

The counsell haveing considdered the great and attrocious crymes committed be James Thrift, first, in menacing the proveist, for quhich he hes gevin his oath, and thairafter for lacerating the leaf out of the publict toun registers ; for which crymes and insolencies the counsell finds that he hes forfaulted his burgesship, and thairfor declaires his burges ticket null in all tyme comeing, and ordeans him to return to prison ay and quhill he find caution of lawborroues to the proveist, under the paine of four hundreth merkes, and ay and quhill he mak payment to the thesaurer of the soume of fifty pounds Scots money for the forsaid fault in lacerating the toun court book.