Reading through this thread again, the biggest takeaway I have is that it's not entirely clear WHY you want to buy a functioning job shop of indeterminate variety. I don't mean this harshly and I may be missing something.
To recap what it sounds like the situation is: You currently have a manufacturing business in the construction field, which has staffing issues, and is not hands-off. You have some product ideas in this field that you're not currently manufacturing, but you're not sure that the market is there to start a production machine shop. You would like to buy an established job shop (you're not sure what type of shop) and run it hands-off with existing customers and some new customers that your shop manager will bring in. At some point in the future, you would like your job shop to build products for your first business to sell.
It isn't clear that you want to BE in the job-shop business, but rather that it's a means to several of ends: having a more hands-off business, and being able to do your own products.
The largest risk I see to your plan to buy a hands-off business is that, right now, you have a functioning hands-on business and some cash. If the hands-off business isn't, and pulls you away from your current business, you could have two businesses tanking.
Not knowing the details, one course of action might be to start by making your existing business more hands-off, allowing you to focus more on new-product development. The machining can be farmed out initially, you can buy equipment as you need it, or look at buying a very small machine shop (1-2 people). There are a lot more of those for sale, and they won't be hands-off, but it would get you a basic complement of equipment (lathe, mill, surface grinder, tooling) pretty inexpensively. The owners of these are usually retiring and the shops go for approximately equipment value, and the owner may be willing to work part time in retirement to get you started up.