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If you locate where the drive axle goes into the differential on the driver side of the transmission at the three o'clock position there is a 17 mm fill plug. Remove this plug the fluid should be just down from the threaded portion of the hole. It uses the same type of fluid that is put into the automatic portions of the transmission. Unless you have abnormal noise in the drive train which would indicate a problem in the differential it's is unlikely that this is going to be the cause of your the late engagement on this transmission. You may want to consider having a transmission flush service done with a cleaner additive perhaps something is sticking in the valve body. If you move the shifter into the L position does it seem to engage and shift normally if you manually shift up through the gear ranges?Skyvisions
The same delay occurs in the lower gear positions. Once the vehicle gets rolling it drives and accelerates fine.
If you are getting the same delay going into the L position and into the reverse position this is not electrical problem. More than likely this is a fluid pressure loss problem or possibly something sticking in the valve body. You may want to consider having a transmission fluid exchange service done where they had cleaner additives to the fluid them flush the entire fluid system out as new fluid is replenished. This is about your cheapest option to try and free up anything it may be binding or sticking in the valve body or clutch pack assemblies. If you have real excessive miles on the vehicle there is a possibility that the clutch packs are just worn out and it's taking too long for the hydraulic pressure to engage the clutches. This may make sense due to the fact that it seems to do better once it's warmed up and everything expands.Skyvisions
Where are the clutch packs located and is this something I can replace myself?