Bee Ghost...Others.... Let me share some of my experiences with trapping over the years. I am not saying that this is the only way, or that it is the best way, I am just sharing how I would do it, from what I have observed.
I don't believe I have ever had a queen come through the funnel. I doubt that she would, but she might. After the bees are going through the tunnel, all entrances are closed off except the front of the trap, and the guard bees are on the landing board, the first thing that happens is cleaners will clean the brood combs you put in the trap and the trap itself. When there are lots of cleaners in the trap, and bees are going and coming freely, place a frame of unsealed brood (NO BEES) in the trap. Don't seal off the end of the tunnel just yet. Let it be for a few days. Things will pick up very quickly. Nurse bees will move into the trap to tend the brood, more cleaners and fanners will move into the trap, workers will continue to come through the tunnel, gather pollen and nectar, and some will return to the feral colony, while others start to deposit nectar and pollen in the brood combs you provided. The queen will come into the trap to investigate the unsealed brood, in essence, wanting to know who is laying eggs in her house.
Numbers of bees will tell you a lot. IF, withing 24-48 hours you do not have 3 to 5 pounds of bees in the trap, (6-10 pounds is not uncommon the first trapping in the Spring, on a good source), it tells you a few things.
1. The colony is too weak to trap. If this is the case, just leave the trap in place and let it build up.
2. The trap is too far from the feral colony brood nest for the additional nurse bees, queen, cleaners, etc. to come out into it. Wait and see if the hive builds up and needs more room. Watch to see if workers are storing nectar in preparation for using this area as honey stores area, rather than another brood chamber, which is what you want.
If you do not find the queen in the trap or the queen does not start laying in the trap,
1. the trap may be too far from the brood nest. If this is the case, most often you will see formation of queen cells from the open brood you provided. The bees that moved out into the trap consider it a seperate place, rather than an integral part of their colony, and will try to make themselves a new queen. Once those cells are formed and capped, then, they will likely bring the queen out to investigate. If so, you will see the queen cells chewed up, or destroyed. If nothing happens to those queen cells, , those queen cells will hatch if you leave it in place, and you will have two colonies with a shared entrance. Your trap, and the original feral source. At his point, you will need to close off the end of the tunnel so bees can come out of the feral source, but, cannot go back. Get enough bees, and move, install a new queen, or, if those queen cells are still capped, let them continue making themselves a queen.
2. The queen does not need additional room to lay eggs. Again, allow the colony to build up and need additional brood combs, and area to lay.
If the tree is already crowded, the bees and the queen will immediately move into your trap because here is additional brood combs, and space for eggs and storing honey. This is what normally happens to a good, strong colony. 24 hours and you have 3-6 pounds of bees. I don't know that the bees would "push" the queen out, but, more likely she will just move out to another place to lay eggs. Another brood chamber.
Hope this has been helpful. If you have specific questions, just let me know. Happy to share my experiences with trapping.