Nginx handling relative paths causes 404 errors

The relative paths are added by your backend application. nginx does not touch the paths in any way.

If your backend application uses relative paths, then your frontend URL must be at same depth as backend URL.

In your first example:

https://lfportal.mohavecounty.us/bos/0/doc/1652027/Page1.aspx

The URL is on fourth subdir level. This means browser can resolve ../../../ to /bos.

In your second example:

https://lfdocs.mohave.gov/bos/search.aspx?dbid=0&searchcommand=%28%7B%5BBOS%20Agenda%20Packets%5D%3A%5BMeeting%20Date%5D%3D%2211/23/2020%22%7D%20%26%20%7B%5BBOS%20Agenda%20Packets%5D%3A%5BMeeting%20Type%5D%3D%22Special%22%7D%20%26%20%7B%5BBOS%20Agenda%20Packets%5D%3A%5BItem%20Number%5D%3D%22Item%20001%22%7D%29%20

The URL is on second subdir level. Now, browser tries to resolve ../../../ URL, and it ends up being / URL.

My recommendation is that you replace the relative URLs with site-root relative URLs: /bos/Helper/TileData.aspx?reposName=MohaveDocs&docID=1652027&x=0&y=1&pageNum=1&scale=3782&ro=0&time=1607098159588&showAnn=1&pageID=7493796&search

Another issue with your URLs is that the ampersand characters are URL encoded, which might lead to undesired end result.