Ranch,
That part is your "control valve". It fits into the pump and the other 2 rounded ends, fit into the "control forks". Yours just came apart. The reason it came "apart", is because the "control forks" loose their strength, over years of use, and allow the 2 rounded ends, of the "control valve" to slip out.
You can reverse the procedure and reinsert things.
I recommend taking the other "inspection plate" off and get someone to also help, as the forks, need to spring sideways (by force), to get the round ends, back into the holes in the "forks". I however did it alone, but it takes 2 hands through one inspection cover, or by tacking the seat off, you can get a hand in each inspection cover hole.
With the "control lever" all the way down (control rod to rear). put the control valve baxk into the pump. Next place one one rounded end into the fork. Next, move the inserted round end as far as you can insert it and at the same time, bend the remaining end of the fork, as wide as you can and pull and push the other rounded end of the control valve into the hole of the "control fork". A couple of cuss words help.
When all are connected the control valve, should move in and out and the lift work
To make sure this doesn't come apart again (as it will happen), Put a "plastic electric Tie-tie" around the forks, to hold the 2 forks together, against the 2 round ends. Some innovative way may be needed, to keep the plastic tie, from slipping off the ends of the forks, however the rounded ends of the forks are sufficient, to accomplish this.
"Happy fishing" in the oil and pertending you "Houdine".
BTW Feel for crud in the bottom of the oil, as most PO don't change oil, or drain water on the bottom, and your next step is "to drain the oil from all three plugs underneath, spray wash out all gunk and replace with new oil. Be prewarned that this cleaning also stires up other crud, and you may exoerience some stuck valve problems until all settle down again.
PS, I just cracked open my plug under the pump and drained about 2 quarts out, to visually look to see if there was water at the bottom of the oil, and to flus out accumulated "crud. (good maintenance issue as I use the tractor for snow plowing. I also make sure my tractors are housed as rain water can enter, thru the shifter boot ,thru the "draft control spring" and condensation.
Charles Krammin SW MI
Hope some other forum member, posts a picture of the control valve and contro rod in pump.