First off, why is it even important to spot core from non-core business activities? If you are a B2B entrepreneur, then you have probably stumbled on the realization that businesses are much more amenable to outsourcing non-core but important business activities to outside vendors like yourself. For a given industry some activities are evidently core and some very clearly non-core. However, a large majority of activities are somewhere in the gray area in-between. As a B2B entrepreneur, how do you spot such activities? One indication is whether or not the business has put their production resources (engineering team, manufacturing plant, etc.) to work on that activity. If they have, they consider this a core activity. It'll be hard to convince them to outsource it to you. Of course it is entirely possible for some other company in the same industry to consider this non-core!
Below is an illustrative example that helps me anchor this concept.
Consider two hypothetical Indian resturant owners - Mr. Khan and Mr. Singh. Mr. Khan runs a brisk lunch kitchen in the middle of downtown. Mr. Singh runs a high end dinner restaurant in an exclusive neighborhood. Both have their chef and kitchen staff fully engaged in cooking and serving Indian food. It is a core activity. If I propose supplying pre-cooked Chicken Tikka Masala to their doorstep every day, they'll refuse. That is, after all, what they do. On the other hand, consider payroll managment for their contract employees. It is clearly non-core. They'll be happy to outsource that task to a company like Zenefits or one of its clones. But the interesting tasks are somewhere in between. Instead of supplying pre-cooked food, lets say I propose supplying fresh produce to their doorstep every week. What would their reactions be? One way to predict their reactions is to look at how do they currently buy their produce. If their chef/kitchen staff does this, then they consider this core and will not buy your delivery service. If they have somebody else outside of the core kitchen staff do this, then you have a shot. So lets find out.
Mr. Khan asks (forces?) his teenage son to buy groceries for the restaurant every week. When lunch hour starts on week days, his no-nonsense chef needs the ingredients ready to use. Mr. Singh's chef on the other hand personally goes to the local farmer's market to hand pick the freshest produce he can find to prepare the delicate the falvors that he is going to charge a fortune for. Who do you think is a better prospect for the grocery delivery service?
Of course the above is a contrived example, but based on my (admittedly limited) experience in B2B sales in the last one year, a rough (i.e., not 100% accurate) indicator of non-core activity is whether or not your prospect is putting their production resources on it.