Honestly, OP, it sounds like he was drifting for a few years before your Mum died. You say how can you persuade him when his mum couldn't - well, you love him and will help him, but you won't be a bottomless pit of understanding and forgiveness in the same way as a mum. So hopefully he'll be more proactive, because he knows his safety net is to some extent reliant on his stepping up now.
I don't think being a bit aimless at this age is unusual, and it may be that a year or two in the workplace, doing a dull job, will stimulate him to want to get back into education. He may even find he does an apprenticeship and enjoys it - plumbers and electricians need to be bright, after all, because the danger of screwups is so great. A sibling of mine dropped out, then after a time of pizza-delivering trained to be an electrician on an apprenticeship, and then went back to uni when he turned 30. Graduated with a 1st in engineering this last year. Life is a long time when you're 19. He's plenty of years ahead to consider what he wants, long term. Right now, he needs to find a way to support himself, and a structure to his life.
Glad you can see your way to helping him, and glad you're being level headed about it, too. It could be just what he needs - love and support from family, with clear expectations and boundaries. It'd be so easy to slump into a horrible depression in his shoes. He's been orphaned as a teenager.
hope the future is brighter for him, and you. And I'm also aware that your dad must have died when you yourself were very young, given he was a baby at the time. That must have been horrendous, too, and I'm so very sorry.