Forum Discussion
You may be able to create your client auth certificate with the appropriate intermediate/root certificates appended. You will need to test this - I'm not sure if it will work.
Alternatively, on version 13.1.0.x, you could enable In-TMM Monitoring
K11323537: Configuring In-TMM monitoring
This new feature allows TMM-based HTTPS monitors to use an existing server-SSL profile to establish SSL/TLS to a pool member.
However - this comes with a caveat...
Once you enable In-TMM monitors via the db variable, you will need to update all existing HTTPS monitors to use a suitable server-side ssl profile. There is no current migration process from bigd (OpenSSL-based) settings to TMM (F5 crypto) monitor settings, and unmodified HTTPS monitors will fail in the config due to an incompatible cipher string.
YMMV