Yes, a blinking S light can indicate some fault in the transmission (as can your D4 light) or maybe just in the wiring. I'd suggest you go to an experienced independent Honda repair shop and have them read the codes (done through counting the blinking lights)
Here's what the book says:
When the A/T control unit senses an abnormality in the input or output
Systems, the S indicator light in the gauge assembly will blink at
equal intervals and the LED display on the A/T control unit will blink
a problem code when the ignition key is turned on. However, when the Service Check Connector
(located to the lower right of the glove compartment) is shorted with a
jumper wire, the S indicator light will also blink the problem code
when the ignition switch is turned on.
When the S indicator light has been reported on, short the two terminals of the Service Check Connector together or pull the passenger's side carpet down from under the dashboard. Then turn on the ignition switch and observe either the S indicator light or the A/T control unit LED display.
Problem codes 1 through 9 are indicated by individual short blinks,
Problem codes 10 through 15 are indicated by a series of long and short
blinks. One long blink equals 10 short blinks. Add the long and short
blinks together to determine the problem code. After determining the
problem code, refer to the electrical system Diagnosis By Symptom / Symptom-to-Component