Take it to get the gearbox replaced.
There are several things that can cause your 2005 Jeep manual transmission to shift hard between first and second gear. The most common cause is a malfunctioning shifting fork.
The biggest problems of why a jeep wont go into third gear is either that the shifting fork for third gear is worn or bent or the sycronizer or gear itself is worn out and needs to be replaced. Once you take the top of the transmission off where the shifter is located you can see the whole transmission gears and inspect the shifting forks. A general rule of thumb is to make sure the transmission is in second gear before taking the top off. This will make it easy to take off and rerattach the top of the transmission cover and align the shifting forks.
A 2000 Jeep automatic that is not shifting correctly after it gets hot might have something wrong with the speed sensor that is located in the transmission. The speed sensor tells the transmission what gear to shift into at certain speeds.
Your synchro is most likely going bad, the same one works for 1st and 2nd so 2nd should be giving you trouble too.
The first cause of the jump out from one to other gear is the loose shifter fork, which connects the shifting linkage and gears of the transmission. The second cause is loose shifting linkage itself, which connects the gear shifting knob and shifting fork. The shifting linkage and shifting fork become loose due to the rapid changing of gears from one gear to other at high speed of vehicle. The third cause is the misalignment of shifting linkage to the shifting fork.
Down from neutral for first gear and up for the rest
maybe you broke something!
Your bike gear may not be shifting properly due to issues such as a misaligned derailleur, worn-out cables, or a dirty chain. It is important to check and adjust these components to ensure smooth gear shifting.
Microshift is a type of gear shifting mechanism that allows for smaller, more precise adjustments in gear ratios compared to traditional gear shifting mechanisms. It uses a different design and technology to achieve smoother and more efficient gear changes.
check the exhaust system
The revoshift friction system in bicycle gear shifting allows riders to manually adjust the tension of the gear shifting mechanism, providing more control over the shifting process. This system enables riders to fine-tune their gear changes to suit their preferences and riding conditions.
There are several things that can cause your manual transmission not to shift out of first gear or reverse. The most common cause is a broken shifting fork.