was he involved in politics?
Yes, in 1660.
William Bruce (architect)
Following the restoration, William Bruce was appointed Clerk to the Bills in 1660, and Clerk of Supply to the Lords in Council in 1665. 
when was architect william bruce born? Around 1630.
wiki:2658109
William Bruce (architect) [SEP] Political career
Following the restoration, William Bruce was appointed Clerk to the Bills in 1660, and Clerk of Supply to the Lords in Council in 1665. Both were lucrative positions, involving collection of fees, from Parliament in the first case, and from petitioners to the Court of Session in the latter. Meanwhile, Sir Robert Moray had established himself as a courtier and scientist at Whitehall, London, and employed Bruce as a trusted messenger between Whitehall and the Duke of Lauderdale, Secretary for Scotland. Moray later served on the Treasury Commission for Scotland, as did Alexander Bruce, now Earl of Kincardine. Bruce reported to this Commission as a revenue collector, and benefited from the patronage of its members.