My truck has recently developed an annoying starting issue. It only gets driven occasionally, but recently has developed this issue. Whenever I try to start it I get nothing until I pull up on the shift lever, then it starts fine. My question is if there is something I can adjust/replace to correct this annoying issue. I searched, but didn't find anything relating to this.

 

It sounds like the park/neutral safety switch is out of adjustment.

I'm not sure if this will help, it's from a 2000 but the same engine/transmission:

Gearshift Adjustment Procedure

(1) Shift transmission into Park.
(2) Release cable adjuster lock (underneath the power brake booster) to unlock cable.
(3) Raise vehicle.
(4) Slide cable eyelet off transmission shift lever.
(5) Verify transmission shift lever is in Park detent by moving lever fully rearward. Last rearward detent is Park position.
(6) Verify positive engagement of transmission park lock by attempting to rotate propeller shaft. Shaft will not rotate when park lock is engaged.
(7) Slide cable eyelet onto transmission shift lever.
(8) Lower vehicle and check engine starting. Engine should start only in Park and Neutral.
(9) Lock shift cable by pressing cable adjuster clamp down until it snaps into place.