[Elle_Rav4]

For the mystery part that has three wires:
I think this may be simply a holder for the wires going from the transmission solenoids (in the bottom of the transmission casing) to the Rav4 computer (located under the radio). I do not think you have to do anything special when re-assembling it.

In the first attachment, see page AX-17 near the top for a drawing.

In the second attachment, look at the connector circled in green and labeled "E 1." E 1 is said to be the "electronically controlled transmission solenoid" (a somewhat misleading name?).

In the third attachment, look at what is circled in green. Three wires are shown for a 2wd Rav4.

 

[Elle_Rav4]

For the speed sensor, open the attachments and do a keyword search for "vehicle speed sensor." Some drawings will come up showing the location on certain 1996-2000 Rav4 transmissions. I think your tranny is an A241E? The latter is supposedly similar to the A540H.

The drawings in the attachments may or may not show your Rav4's speed sensor's location. The three wires that connect to the vehicle speed sensor have the following colors:
-- Light blue with black stripe
-- Red with yellow stripe
-- Red with light blue stripe

 

[Elle_Rav4]

I googled on {"A540H" "transmission"} and similar and a number of manuals came up.