DETROIT— Tesla Inc. was absent at the annual auto show here this month, but its new Model 3 sedan was still a hot ticket.

Tucked away in the convention hall’s basement, far from the new Chevrolet Silverado pickup and Toyota Avalon sedan displayed on the main floor, Caresoft Global Inc., an engineering firm based in the Chicago area, showed off a Model 3 chassis.

It is one of several sedans Caresoft has purchased from third parties since November, with the goal of studying them and selling data and technical insights to Tesla competitors—for upward of $500,000.

“There are people who flew down from China just to have a test drive with us,” said Caresoft business manager Prideep Subramaniam.

A shortage of Model 3 sedans has created a frenzy among curious competitors, Tesla enthusiasts and auto reviewers to get their hands on the electric car, which starts at $35,000. Tesla was supposed to be making over 5,000 Model 3s a week by now—instead it delivered fewer than a total of 2,000 the past two quarters.