Rear diff

Hello new to titan talk. I need to see if anyone can answer a question i have about the rear axle of my 2010 T crew cab sv 2wd? Ok her's the rip i bought it used, salvage title, truck in great shape. It has the vdc button and when i turn it off, while on dirt roads when i hammer on it it leaves equal length tracks. I know i can jack up the rear and turn the tires, etc. Problem disability prevents me from doing so plus lack of eq. Could pull cover i know, just changed out the gear oil. Was told by Randy's ring and Pinion that lsd's had been put in some t's? Also some open diffs can leave two tracks?????? No truck with an open diff ever did. It's possible previous owner put a true trac in who knows? What say you guys. Thanks for any help.