Jonathan_c If you're performing SSL termination on the F5 you should be able to do this by going into the SSL profile and disabling session mirroring. You will have an issue if this profile is used across multiple VS and only need to do this on one of them but you can always create a copy of that SSL profile and name it something slightly different so that it will only be for this one VS in question. If you do not have SSL termination you can go into the virtual server and disable connection mirroring. These two are outlined in this article.
https://my.f5.com/manage/s/article/K08005980
Cirrus
