Thanks to some inspiration from another post, I think I figured out what I was doing wrong.
For the second node, it should not be initialized. Instead, the server should be started:
vault.exe server -config vault.hcl.
Then, join the second node to the first:
vault operator raft join http://172.24.32.184:8200.
And finally, unseal the second node:
vault operator unseal (Here be sure to unseal using the unseal keys from the first (leader) node.)