I am pleased to report that, thanks to an article in the Santa Cruz Sentinel found by Bob Beck of Pasatiempo, we know now where Mackenzie's par 3 course was located in the SF area. It was a private approach and putt course built for SF furniture retailer Gustave Lachman (of Lachman Bros) on his 15 acre property in Hillsborough in San Mateo County, at 1225 San Raymundo Road. Lachman built a 20 room Tudor style mansion on the property, which was completed in 1932. Mackenzie's short course was nine holes and was apparently lit for night use according to one later article I found. The course was officially opened in July 1932.
By 1944 the property had been reduced down to 3.2 acres which would have meant the course was gone, replaced by subdivided houses. The house built by Lachman still stands though and it is quite spectacular. Sold in 2010 for around $8 million.
If there is any interest I can post the article and some pictures of the house.