Here's some information from older posts on how to check the operation of the three-position solenoid on the auto transmission:
"The usual problem with rough downshifting automatics in these 113's is non-functioning or mal-adjusted three position solenoids or linkages. Oftentimes the intake butterfly stop screw is mistakenly used as an idle adjustment scew. If this happens the transmission solenoid switch on the intake is thrown out of adjustment causing the three position solenoid on the transmission to not function properly or not function at all. This solenoid should soften that last downshift when working properly."
"Joe Alexander: You can remove the access cover on the passenger side tunnel area and observe the movement of the transmission linkage and three position solenoid, while test driving the car. You will need a second person and a flashlight. The kickdown or passing gear switch on the floor under the accelerator pedal must be engaged and working to activate the solenoid. When fully depressed this switch is engaged and it energizes the three position solenoid which will move the control pressure linkage on the side of the transmission. This linkage changes the control pressure at the modulator assembly on the transmission and causes the downshift. Make sure you have power going in and out of the accelerator kickdown switch when it is depressed. Next try observing the operation of the three position solenoid. Position one at idle in gear, position two after driving off, position three at full throttle (accelerator fully depressed and switch engaged). If all seems to be working ok then more complicated adjustments can be made at the modulator or the linkage on the transmission (do this only as last resort and after everything else is checked out). Be sure to check the switch on the venturi. It is a brown bakelite switch with two wires going to it. It is mounted on the intake venturi,a little further up from the air cleaner. With the ignition on, car in gear, the switch should have power at both wires (closed switch). After slightly moving the throttle open the switch has power at only one wire (open switch). Your transmission will never shift right unless this factory setting is restored."
Cees Klumper in Amsterdam
'69 white 280 SL automatic