1996 Tacoma 2WD Auto Transmission 4 speed, want shift from 2nd to 3rd

My first truck ever, bought off Craigs List, 1996 Tacoma 2WD 2.4 CC 2RZ-FE EFI
Has 150K, Runs like a top with one exception. Auto Transmission will not go from 2nd to 3rd.
I changed the tranny fluid. I can get it to go from 2nd to 3rd by manually shifting the column mounted shift lever from 2nd to 3rd once I get up to about 30 MPH. It will then smoothly go into third. The truck I am told originally came with 14 inch rims. Now it has 15 inch rims. When the speedometer says I am doing 35 I feel like I am going 45 or better. Occasionally it will go from 2nd to 3rd if I punch it but it doesn't shift to 3rd on it's own until about 42 miles an hour and even then not consistently. If I manually shift from 2nd to 3rd it will easily smoothly go in about 30 mph.

Any ideas on basic troubleshooting starting points. The truck and tranny runs strong other than this. The transmission fluid was very dirty when I bought it.

Is there an adjustment, mechanical I can set to tell it to shift at a slower speed?

Thanks very much for any ideas that might be offered.

 

If you put the 14's back on will it shift correctly?

 

Had the 15" rims on it when bought it used, he told me originally had 14"s but he had sold them. Thanks for the suggestion. I am not opposed to putting 14 inch rims on it, or lower profile tires going to get new tires anyway. Going to be a street truck for putting around the neighborhood, Home Depot etc taking care of mom's garden. I was hoping there was a mechanical linkage that could be adjusted/set to shift at a lower rev. I have already found out that the ECU is not programmable/flash.

Thanks very much,

 

Speedo is mechanical too and will be off unless you change the speedo gear in the transmission. If you need tires then I would suggest you go back to 14's or at least for with the same height in tire as what came on the 14's so that your rotating speed is the same. The steel 14" wheels are super cheap on ebay btw