Force cluster to elect new master node

I added a master-only node to my cluster.
How do I trigger the active master role to the new node?
I want to leave at least 2 of my data nodes as eligible masters, but have my cluster prioritize use of the dedicated master.

There is no need to do this. You should not care which of the master-eligible nodes is the active master as this can change over time. The active master node does very little in most clusters so will not add a lot of load.

If you are concerned about one of the master-data nodes being elected as the master and have seen some impact you should look to have 3 dedicated master nodes instead.

The currently elected master node is also an ingest for Elastic Agent clients so CPU is always really high (90-100%).
Elastic support recommended a dedicated master to improve performance, but now it's just sitting there pretty much doing nothing.

You should load balance the indexing load across the two data nodes so they are reasonably evenly loaded and not send all traffic to just one of the nodes.