Your ancestor belonged to at least two regiments during the W1812: the 24th Regiment of United States Infantry and the 2d Rifle Regiment. The 24th was raised in Tennessee and the western territories and served at Fort Meigs in 1813. Bird Lavender probably was there during the second siege of Fort Meigs (and maybe at Fort Stephenson) and was most likely part of the invasion of Canada, but was probably not at the Thames. After the Thames, detachments of the 24th served in scattered locations: some at Niagara, some stayed at Detroit, and some were in the Missouri Territory. If Lavender enlisted for 18 months, it is quite likely that he joined the rifle regiment when his enlistment was up. In March 1814, Congress had created 3 additional rifle regiments, of which the 2d Regiment was raised in Ohio, Kentucky, and Tennessee. Benjamin Johnson was a company commander in the 2d Rifle Regiment. The 2d Rifles did not do much. By the time the war was over, only 3 companies were ever raised. Those three companies(Harrison's, Desha's, and O'Fallon's) served at Malden.
There are a couple of things in your note that are misleading. The 24th was not a light infantry regiment; aside from the 4 US rifle regiments and some militia units, the US had no purely light infantry units. The 2d Tennessee Regiment sounds like a militia unit and Lavender may have belonged to it before he enlisted in the 24th. On the plus side, there is certainly a strong Tennessee connection.
If you know the name of Lavender's company commander in the 24th, it's possible that you may be able to find out where he was in 1813 and 1814. Maybe the Tennessee state archives has the muster rolls.