You want to send a HEAD request to skip the response body, but you can’t do that. Instead, send a GET request which will never return a body: one that was modified since the future. You’ll always get a 304 Not Modified, and get the Last-Modified response header.
GET /data/wow/connected-realm/5/auctions?namespace=dynamic-us&locale=en_US&access_token=ZZZZZ HTTP/1.1
Host: us.api.blizzard.com
If-Modified-Since: Sat, 01 Jan 2050 00:00:00 GMT
HTTP/1.1 304 Not Modified
Battlenet-Schema-Revision: 5
Date: Mon, 02 Mar 2020 18:19:52 GMT
Server: Apache-Coyote/1.1
Last-Modified: Mon, 2 Mar 2020 18:06:26 GMT
Battlenet-Namespace: dynamic-us
Battlenet-Schema: auctions
content-length: 0