The L113 is not listed on the page I linked; but it's the same as the 113 except that the shaft is longer to fit through the top of a guitar (rather than a piece of sheet metal). The schematic for the L113 is number V on
this page. As you can see on that page, not all jacks are the same. If I understand/remember correctly, the make circuit on the L113, breaks the ciruit to the battery when the instrument is unplugged, saving battery life.
How far off is the jack from fitting in your bass? If it's off by just a little, you may be able to bend the spades that the wires are soldered to, carefully, with a couple of needle nose pliers. If you have a camera handy, some pictures might help; some of the folks around here might have some suggestions if they can see what the problem looks like.