But to my GMB listing?Yes backlinks is necessary, website is also important. You can implement schema.
As in just Backlinks or Citations?Yes and use the NAP with same.
- Link using your CID URL with raw URL or exact anchors
- Map embeds
- Driving directions
- (co)-Citations
Use these in guest posts, PBNs, PRs, web 2.0s, niche edits (if possible) and digital PR pieces along with your typical links to your location pages.
Building a backlinks for GMB page isn't necessary, take it as a option. What important for GMB page is, Business Citations and Press Releases, but use the same exact NAP that's on your GMB Page. Also, request your provider to use the NAP on all listings. Map Embeds helps as well.
Is linking to the CID still working for you? I've found it's lost it's power the past few months.