The manufacturer of the old style connector with round pins discontinued production of that style connector. Replacement incident illuminators for BM & BMK are now supplied with the male/female receptacles so that the discontinued connectors can also be replaced. However, the new style receptacles only fit newer BM/BMK Series bases that have a thinner upper plate thickness. In other words, the new style receptacle is not long enough to pass through the older style casing.
Unfortunately, short of machining the base on a mill, there is no acceptable fix for this problem. We can suggest removing the old connector, and epoxying the new receptacle in place. Once installed and fully cured, one would still need to be careful yanking the male connector out of the receptacle.
Fortunately, this connector does not get cycled too often and you may elect to use any other 2 conductor panel mount connector that can pass through at least 10mm of casting.
The new connector fits only a 6.8mm panel depth.
Connector Part Numbers
New Style Male Connector
New Style Female Connector