The Ethernet interface on the RE's are for out-of-band management and aren't routed interfaces. In other words, you can not (not are you supposed to) run routing protocols over them. More info here.
As for the high availability, you have a couple of options:
1. Use the defaults. If you don't configure anything, re1 will kick in 300 seconds after re0 becomes non-responsive. If you aren't using commit synchronize, this may not necessarily be a good thing :-). Also note that without GRES enabled, re1 would take some time to boot, load software into the PFE(s) and become fully operational.
2. Enable GRES (routing engine graceful switchover) as described in here. When GRES is enabled, the backup re (re1, normally) would already have JUNOS loaded and the default timeout would be down to 2 seconds; effectively making the switchover period much faster. Without NSR, your protocols will still flap, of of course.
3. Enable nonstop-routing. This will, for supported protocols, add protocol state/adjacency replication on top of kernel replication introduced by GRES. With this setting (and depending on your configuration / usage), a RE failover would be almost fully invisible / undetectable by the neighboring devices.
I personally also configure the following, regardless of the option chosen: