I dont remember exactly when they close but I seem to recall that we needed to be there much earlier than I had hoped. Something like 5pm? Someone else can weigh in on that, but as for time, I traveled with two other Americans. I am jewish and have a zillion israel stamps in my passport and my travel partners are not jewish and had no stamps. It was clear that my partners were what was slowing us down. I would say it took us 45 minutes to get out of Israel, about 2 minutes to get into Jordan, then 2 minutes to get out of Jordan and about 2 hours, maybe a little less to get back into Israel. The Jordan/Israel border on the entering-Israel side is one of the more frustrating in Israel (the world?) but we did get through without any suggestion we wouldnt despite the endless hoops they made us jump through. We were very polite but also be respectfully firm. Of course it depends on where you are from, and what religion you are. You can do simple ethnic-math to figure out how they will handle it. Being turned away generally will not happen unless you raise a particular flag. Being alone is an issue but not reason to be turned away so that by itself is not sufficient by any means. Having paperwork to support clear cut locations in israel that show where you are going is helpful (lots of paperwork of a hotel reservation for example, or a tour operator etc,) it also helps to have israeli friends, in israel, who you can call ON THE CELLPHONE right there at security (make sure they know why are taking out your phone!) to talk to the border guards and make them realize you are not some loner with no associations.
As for being on foot, that does not matter. Everyone is on foot since your car or cab drops you on one side and you get a car or cab on the other. Just tell them you are catching a cab on the other side -- going both ways. If you have an israeli cab with an israeli driver waiting for you when you come back, that can only work in your favor especially if you can get him to show his face. I realize some may disagree with these very specific and petty tactics but they all work. I'm a journalist who has covered that region for years and its all about how you make people feel and what they perceive.
Edited by: guywithcat