That is normal operation for 1992 2.3l SOHC Lima engine
1989 to 1994 2.3l Lima uses only 1 coil pack when starter motor is active, passenger side/exhaust side coil pack is active
This was done to give a hotter spark to 4 spark plugs when starter motor drops voltage down to under 10volts while cranking
The drivers side/intake side coil pack should start working when RPMs are above 400, cranking speed is 200rpm, so after startup this coil pack should start working
See attachment, at bottom, ICM pin 6, Dual Spark Inhibit(left is driver's side coil pack)
1995 and up 2.3l/2.5l have both coil packs working for startup
1974 to 1988 the 2.3l Lima engines used only 4 spark plugs, so just using 4 spark plugs for start up is not an issue
Popular myth for dual spark plugs is that they "alternate", no
Point of dual spark plugs in ANY engine is that it produces more power than single spark plug, so BOTH spark plugs fire all the time or there would be no point in having dual spark plugs
On startup, horse power is not the issue, hot spark is better, but it was found to not be needed so dropped in 1995
4 valves per cylinder produces more power than dual spark plugs, so 4 valves is a better use of head space and dual plugs fell out of favor as DOHC engines came into use