Why does the Elaboration Likelihood Model not account for truthfulness of the message?

Not my area, but an interesting question.

The Elaboration Likelihood Model appears to divide messages between that which is true and that which is persuasive. If you are intent on determining whether a message is true, it must go the rough the central route which will take protracted effort.

However, very often we are less interested in what is true and more interested in taking cues from others so that we avoid the laboursome effort of intensive thought.

To answer your question, if the message is persuasive, then no about of truth or falsity of which you are unaware will influence you.

I could not see it in the article, however, I imagine that if you were a priori aware that a message is false, you would naturally be more circumspect about allowing a false argument to be persuasive.

Modern advertising seems to revolve around persuasive arguments rather than truthful arguments (I'm not saying they are false, but the investment effort is making the commercial persuasive rather that factual).

The following except from Kitchen (2014, page 2034) clarified the issue for me.

The premise of ELM is that when elaboration likelihood is high, information processing will occur via the central route. Resultant attitude formation, change or endurance is derived from extensive consideration of the message arguments and will be more persistent (Haugtvedt and Petty, 1989) and predictive of an individual’s subsequent behaviour (Petty and Cacioppo, 1983). When elaboration likelihood is low, processing occurs via the peripheral route. The peripheral route to persuasion requires little cognitive effort, instead relying upon peripheral cues such as source credibility and heuristics (Petty and Cacioppo, 1983). As such, attitudes formed via the peripheral route are relatively unaffected by argument quality, are temporary in nature, and are not as predictive of subsequent behaviour as those formed using the central route (Petty and Cacioppo, 1983).

Kitchen, P. J., Kerr, G., Schultz, D. E., McColl, R., & Pals, H. (2014). The elaboration likelihood model: review, critique and research agenda. European Journal of Marketing. https://doi.org/10.1108/EJM-12-2011-0776