Wow, that MiniUSB does have "character".
Okay, hook up the MiniUSB to the Arduino Mini GND, 5V, RX, and TX pin for pin (yes, TX -> TX, RX -> RX...). For the auto-reset, you are going to need a 0.1uF ceramic capacitor going from the RTS on the MiniUSB to the R (Reset) on either side of the Arduino Mini. If you do not have a 0.1uF on hand, you will have to manually reset when you upload the sketch and the "Binary Sketch Size" appears in the info window, press the reset button.
It does indeed. Thank you for your fast response. I'll need to track down a supply of those things. (The R5 has its reset button on top, the R4 does not.) So that's what I need to do. I originally thought the cap I chose from my collection was
the right size, but apparently not.