When using auto primer I usually do 2 heavy coats, next day sand, 2 lighter coats, next day sand, 2 light coats, next day sand. leave for a few days before doing colour. It is slow to dry even though it looks and sands like it's dry, you can have it looking glassy in the afternoon but grain showing again in the morning. I think the timber absorbs the thinners, swells, looks smooth, then slowly dries out and contracts again. Lets face it , it wasn't really made for use on timber, but I have katana sayas's (sheaths) I painted 10 years ago with auto paints and still look the same as the day I finished them so it does work if you leave plenty of drying time.
I'd sand it till it's smooth again, or very close. if you just have small patches of grain, give those areas extra coats and sand them. If you are using a gun,make a heavy mix and leave plenty of drying time
On my ES I found the areas I'd dyed where drinking up the clear, so I had no option but to keep putting clear coats on and sanding them between. (2 coats in the mornig, sand, 2 coats at night leave till morning ..sand.) I got it 95% smooth, I could have kept going but it kinda looks a bit "genuine" as it is.