Ahh, poor lad. Do bear in mind that he very much might feel that he SHOULD have a plan. Kids that are on this academic treadmill all the way through school, and pushed towards uni after A-levels have been kept moving forwards all the time, busy busy, aiming for this "grand plan" of adult life, and it can be scary when suddenly the "grand plan" seems to have gone wrong.
When you're feeling really lost, sometimes you just don't know what you actually really deep down want to do, but feel like you should be doing something so you grasp at the first sensible-sounding thing that comes into your head, or that others (who you think know better than you) suggest to you. Your DS might be justifying finishing the year to himself because "it's only x amount of weeks" etc etc. But maybe in his gut he's decided that engineering isn't for him, he doesn't think, but now he's stuck because he doesn't know what ELSE he'd like to do and is totally floundering and panicking about the future.
Been there, done that. It's a horrible feeling, just feeling lost like that, and seeing all your friends moving forward with their plans seemingly without a care in the world. I remember feeling quiet and withdrawn when I visited home too, as I just didn't know how to tell my parents I wanted out. I felt ashamed, and lost. The very worst thing that you can do is try to get him to make firm plans at this point. It's ok for him to not know what the hell to do for the best and to take time out to think about it, NOW if he needs to, without any pressure at all.
The only thing that he really needs to hear now when he's feeling like that is that he has the option to drop out at any time, even today, and that you are TOTALLY ok with that. He could go and see the all the counselling people and tutors that he wants but if he's really already decided in his gut that he absolutely doesn't want to be there, you need reassurance that he's not just going to feel forced by well-meaning advice to get through this last term, because if he is feeling as low as he sounds, the pressure of getting through, with exams etc, feeling lonely etc, having to make decisions and plans to transfer on top of that, might just be too much for him.
The path through life isn't straight. Remind him of this. People take wrong turns, long way rounds, end up going backwards sometimes, some people get lucky and find a short cut, but everybody always find their way in the end.