HZ432 and no heat in one zone
Here is an image from the installation manual of your zone controller:



The fact that Heat 1 and Heat 2 are red means that some combination of thermostats is calling for stage 1 and stage 2 heat.

The lights on the zone are pretty easy to read as well.  A red light means that damper should be closed (no air to that section) and a green (might look yellow) light means that zone should be open (have air flow).

Now, the light pattern you describe means that if everything is wired correctly and all the dampers are functioning, you should have air in Zone 1 only.  The red zones should be closed and not have air.  However, there are two types of dampers - normally opened and normally closed, and they have to be wired differently so the controller knows how to open them.  If this is a new installation or work has been done recently, it could be wired incorrectly.

If a damper fails, the unit could show a blinking amber light, but it depends on how it failed.  Some types of failures the controller cannot sense.  It's possible that two zones are stuck open so the controller thinks that only one is open, but really there are 3 open.

If you read the manual for the controller, there are ways to test each damper and cause the fan to run.  You can cycle through each zone one at a time to make sure the dampers work and are wired correctly.  Those instructions are on page 13 in the section named "Checkout".  I would have gone with "Testing" or "troubleshooting", but they picked "Checkout"...  I forget if it allows this or not, but be sure not to close all 4 dampers with the fan running.  The air pressure could blow out some duct joints or damage the dampers.

As far as the activity of your two Trane units - this zone controller is designed to have one unit hooked up to multiple zones.  It's not made to control multiple units.  There might be a way to use the various heat and cool "stages" to control multiple units, but then you're really getting into advanced territory.

If you do call in some outside help on this, do what you can to make sure they are very well versed in these zone controllers.  I had two A/C people give me incorrect information on how they work and really struggle to identify a problem with the system.