You have got a decent amount of time to prepare which is great. With my DD1 I only found out about 11+ 4 months before so it was quite a rush and I helped my DD because it was a bit late to look for a tutor. Motivation was not always easy so I sympathise!
Do you know exactly what your intended grammar school tests - verbal reasoning, NVR, maths, english? Make sure you know exactly what will be expected - here there are 2 tests 45 & 50 mins multi choice and only VR but it varies on area. I remember bying nvr papers before I realised there were no nvr papers used in our tests!! So don't waste time on the wrong things although doing standard rather than multi choice to start with is ok. Well I've been happy to use some standard papers I have got before doing multi choice.
I have friends who use a tutor because their DCs work better for someone else than for their parents so that might help. I agree it is good to have a set day or time when you do your 11+ work, your DS will know what to expect - how long it will take etc. and not worry about you hauling him away from a fave tv programme or game! My DS is y5 and he is doing 2 papers a week at the moment but with help when he needs it and not with time pressure. 1 at weekend, 1 during the week. He is happy to do them but as he is our third DC taking 11+ he knows the score and just gets on with it.
Have a grown up chat about how 11+ is hard work and you need to put the effort in- after all, the other DCs sitting the test will be doing that preparation too. If he wants to go for it you can support him but you don't want to nag (too much) you might agree some treats & rewards too. Have you visited the grammar school together?
He might get fed up by the time the test comes round (most do) but hopefully he will be ready by then.
The other thing is (not every time of course) do things in the car on the school run etc times tables, opposites & similar meaning, word games and play wordy/puzzley type of board games such as boggle then you are learning and having fun and try "free rice" website for word meanings and tables.
Are any of his friends aiming to take 11+? Some people do team up for work although there are pros and cons to this.