I suppose you could just download the image and do a "diff -q" or compare an MD5 checksum, or even just file size.
Or use a different tool maybe? I see that rural supports head requests. https://crates.io/crates/rural
Edit: Appears that ht may be able to get response headers. It's sort of a documentation bug. It has a -p/--print option, but the README doesn't document what the arguments are.
Found it.. "ht -p h https://google.com" returns the headers, so you could extract the Etag or Last-Modified header.