Replicating GTM Configurations between HA

Yes, I guess that would be the situation. From reading through a few of these postings and it sounds like it is possible to put GTM on both members of the HA pair.. and then the vip can float the serving IP to get to whichever one is the active member of the HA pair... While GTM does not work with HA, it does its own synchronization between members.. The VIP is a LTM VIP that is HA. And that is what I'm trying to understand.

If it isn't this way.. perhaps another way so that a VIP can be high available service and continues to serve clients routing traffic to any active GTM.

I need the DNS service to remain active even if I take the HA member down for maintenance, upgrades, or other operations.. And yes there is another GTM instance as the secondary DNS. Looking to make each of them HA.