This is a road I drive frequently because it must be one of the most beautiful in the UK. It comes under 'Great Drives' for Europe.
There is only one set of traffic lights and that is at Dunster on a wide streatch. If you are going into Dunster you don't have to deal with them at all. Just bear left as you aproach them and you head into the village in about 2mins.
I'm not sure where the narrow lanes are as the road to Lynmouth is a 2 lane quiet route over the moor and the direction you are going you will be driving on the side of the road against the moor so no drops there. Just take the hills steady, 2nd gear for Porlock hill and maybe 3rd for going down into Lynmouth. Both hills are short but the views and the wild ponies and birds of prey are worth it.
I would suggest you come off your route down at Taunton and drive the A38 for the most scenic and relaxing. It joins the A39 again half way to Dunster.
Also when you leave Dunster about 10mins on drop into Selworthy, a turning on the right between Minehead and Porlock. There's a car park at the top and a walk to the white church and the green which is surrounded by thatched cottages set in woodland. beautiful and really unique. About half an hour should do it. This is National Trust but free.
There is an ice cream van at the top of Porlock hill on the right in a parking area selling local clotted cream ice cream which you can treat yourself to for doing the hill ;-) again, fabulous views.
There is a stop and park at the border of Somerset & Devon with lovely views and loos. Also a pull in where the wild unique ponies graze a bit further on.
Park in Lynmouth. If it's busy turn down to the harbour road and there's another car park at the end less used.
You could take the cliff railway (if you dare) to Lynton to look around. To travel on you have a choice of heading up towards Lynton but continuing straight on which will take you along the Devon coast. It's a bit narrow, steep at the start. If you don't fancy this take the road on the left marked for caravans which is surprisingly quiet but a normal 2 lane road uphill.
I think it's worth tackling as if I directed you away from the hills you have very little good scenery in comparison.
I'll attach a link to an article I wrote about this drive and the National Trust properties.
https://www.tripadvisor.co.uk/Travel-g186369-c218734/Somerset:United-Kingdom:A.Beautiful.Journey.A39.html