To clarify the parts/operation of the delay system:
The part on the firewall is the Delay Shift Switch-Over-Valve.
It is simply [ like all the other SOVs ], an On/Off vac valve that, when electrically energized from the ECU, allows vac to pass through it , allowing vac from the source [engine] to reach the working servo [ Element] at the transmission.
The Delay Shift Element is at the tranny and is the working part at the end of the transmission pressure cable. This is the part that actually holds the cable in a position to delay the shift point.
If there is a signal at the SOV and it is opening [ allowing vac flow] , the element end at the tranny is the likely fault.
For testing, one can take the in/out line of the SOV and put them together with a small piece of tubing [ eliminating the SOV ] to see if the Element itself is operating. [ holding/delay shift].
A vac gauge "T-eed" into the vac line downstream from the SOV
and positioned at the bottom of the windshield for cabin observation is another way of monitoring the SOV/ECU parameters for proper operation.