I posted a couple of months ago asking how to get 14yo DS reading. One of the suggestions was to read at the same time as him and I tried it.
I let him know the plan, we agreed a book for him (not too long or hardgoing - he started with Holes by Louis Sachar ). Most evenings at about 8.30 I give him a shout and we sit side by side on my bed and read in companionable silence for 20 minutes. It works! Youngest dd often joins us. He often ends up reading for much longer as he gets into the book (but no expectation if he's not feeling it). I've kept the whole thing low pressure - it's supposed to be a positive experience. And if he really isn't in the right headspace that's okay. I reckon we manage 4 or 5 nights a week. He's now on his second book. I love the chats afterwards about what we've both been reading.