It could be the valvebody or the transmission but I don't think you need to go to that extreme yet. There are things you need to check first. The valvebody is part of the transmission and actually controls where the fluid goes in order for the clutches inside the transmission to shift the gears.
I would suggest checking the fluid first. If the fluid is low then the harsh engagement into reverse could just be because the valvebody is trying to send fluid to the reverse solenoids but it is "sucking" air and this causes your delay. Then it gets some fluid and it bangs into gear. If it is low, simply adding fluid or having it changed could fix this.
Also, if it is inside the transmission it is most likely the oil pump. If the pressure is low then it will cause the same symptoms but most likely not just in reverse. This is why I think you have low fluid and the issue is reverse is just the beginning. Hopefully there isn't any or much damage done to the internal components and just adding fluid will correct it.
Here is a resource that will help with this. Let me know if you find anything wrong with the fluid and we can go from there. Thanks
Friday, April 12th, 2019 AT 6:05 PM