SSH Key priority

Hi,

I've got an SSH config block like

host target1.internal.network    
       hostname host.external-net.com
       IdentityFile ~/.ssh/public_key_target1.pub
       user target1 
       port 2222

and fallback

host *
       IdentityAgent ~/.1password/agent.sock
       ForwardAgent no
       ServerAliveInterval 60
       User myUser
       IdentitiesOnly yes
       IdentityFile ~/.ssh/fallback_key.pub

which contains a key for all hosts that I don't explicitly specify. 

I was expecting SSH just to take the first identityfile, but it offers both to my target, unfortunately in the wrong order (the fallback first, which gets rejected, and then the right one)

Is there any way to change the order of the keys offered? I thought it was perhaps alphabetical, but renaming the fallback key had zero effect.

Edit: 

Using 

host *
       IdentityAgent ~/.1password/agent.sock
       ForwardAgent no
       ServerAliveInterval 60
       User myUser
       IdentitiesOnly yes

match originalhost *,!*.internal.network
       IdentityFile ~/.ssh/fallback_key.pub

works, but it is not ideal