Odometer stops working and check engine light comes on at same time

most old cars have a speedo cable.
is the odometer dead too. (we need that answer now)

there are 3 class evolutionary systems.
cable
electric sender to cluster
and sender to PCM and PCM drives cluster.
but honda does this on diffr, dates than most cars. (i learned)

so lets do that. we login to alldata.com and look , so can you at any time,
once a month i do random cars.
what engine, sometimes this varies by engine, and trans.
neither stated so Ill toss coin each time.
a/t trans.
1996
has electronic (hall) speed sensor VSS and runs
engine, cruise. odometer and cluster.

the 96 has no speedo cable, and works in modern mode, very advance for this time
also any scan tool on earth fits the PCM scan port
and if VSS is dead, it tells you that with a DTC , vss dead.
saving all that work wondering why it dont work.
see/?
PCM must see it work
and cluster
and cruise
if only cluster fails, and both speedo and odometer then its bad.
if only speedo fails but not odometer , then speedo meter is bad.
its that easy.

The check engine light should come back on at some point.
Chances are the problem is the speed sensor in the transmission.

Drain fluid into a clean plastic bowl, check for brass cuttings or metal shavings in sunlight. If present get complete trans overhaul.

if the speedo is not sending a speed the trans will go into back up mode and the trans will not shift normally check the speed sensor

check the speed sensor on the trans its on the pass side of the car near the right side axle

The cluster is defective.

Most of the time when the speedometer stopps the odometer stopps too it it has the transmission may have troble ( if it's automatic as the speedsenser helps the trans shift as the computer shifts the trans too. the check engine light should be on also if it's not and the odometer is still working the problem is in the speedometer itself and the unit can be shipped off though your ford dealer for repair but I woould'nt do that till the speedometer has been removed unplugged and replugged in to see if it's just a bad connection. The speed senser can fail too but you will have these other problems tha I mentioned. The senser is on the side of the transmission nesr the place the drive shaft is connected to the transmission. If the automatic transmission shifts normally and the check engine lightisn't on the senser is likly to be good.

possible short in dash. have you put an after market radio in it?

sounds like a clogged converter

yes and itys a very common problem yu need to change the speed sensor (VSS) on the trans heres how it comes apart