Hi again, Hoped to see that you'd had more responses. Not yet, but someday someone who knew them may see your post.
I just searched the 1940 census for Maude Trask (also tried Maude Chase) and William Franklin Trask. I can't find Maude. Have you? The 1940 census is free and available at Ancestry.com. Maybe if you search it, you'll have better luck than I did.
If we found Maude in 1940 we'd have her last known address.
This is the only "candidate" I found for William in 1940. This William had been living in the Twin Cities in 1935:
1940 Tracy, Lyon, Minnesota 2nd Street R. E. Klinefelter 60 Sadie Klinefelter 63 Ellen Klinefelter 81 W. F. Trask 47, single, lodger, b abt 1893 in MA, respondent? YES*; no occupation Olga Falseed 47 Residence in 1935 (W. F. Trask): St. Paul, Minnesota (a question on the 1940 census) * means W. F. Trask answered the questions on the census form himself.
About your question about his mental health, in the above census that William is middle-aged (not a kid just starting out), a lodger, unemployed, recently moved to town (within last five years). That is not a picture of a man who is a stable family man/husband and provider. I think if your William had ever been in an institution, he might have gone to the state hospital in Hastings, Dodge, Minnesota. That was the nearest state institution to the Twin Cities, I believe. If you write to the Minnesota Historical Society for institutional records seeking him at Hastings, you should get a reply from them, whether he was ever there or not. (www.mnhs.org)
William died in Hennepin County, so he for sure wasn't institutionalzed in Dodge County then (or maybe ever).
I am puzzled that I can't find Maude. I hope you find out more, and that better information will come from another respondent soon.