Why Does Wilson Believe That Gatsby Killed Myrtle
Why does Wilson believe that Gatsby killed Myrtle in The Great Gatsby?
There are two important points when considering your question: what Wilson observes before the event and what Wilson is told after the event.
First let's explore what Wilson observes. Quite simply, Wilson observes Tom requesting gas for the car he is driving. Unfortunately for Gatsby, Tom is driving Gatsby's car. I find it ironic that it isn't Tom that actually wants to stop for gas, ... it's Jordan!
"We've got enough to get us to town," said Tom.
"But there's a garage right there," objected Jordan. "I don't want to get stalled in this baking heat."
Tom does, however, make the mistake of telling Wilson that the yellow car is Tom's by saying, "How do you like this one? ... I bought it last week." I think these things cement that there is no premeditated plan to kill Gatsby on Tom's part (in addition to the fact that, of course, he doesn't want Myrtle killed). At least there's no plan at this point.
When Myrtle is killed and someone sees it's a yellow car that killed her, Tom gets a bit nervous (and puts himself above his grief for a while to appease his selfishness). He grabs Wilson and tells him that the yellow car wasn't Tom's. Later, Nick reports that Wilson "announced that he had a way of finding out who the yellow car belonged to." Tom said Wilson "was crazy enough to kill me if I hadn't told him who owned the car."
I wouldn't say that Tom "convinced" Wilson. We aren't told that and can't prove that. ... However, we can safely assume that Tom let Wilson's grief-stricken mind do the work for him. And you know what? Tom was happy to do so!
In short, I think it is safe to say that Wilson thinks that Gatsby killed Myrtle because it was Gatsby that owned the yellow "death car," and it was Tom who was glad to share the information.
Wilson believes that Gatsby killed Myrtle because Tom convinced him. If you remember from reading the novel, before their day out, Tom drove Gatsby's yellow car and went to the valley of ashes to buy some petrol. Myrtle saw this happen from where she was in the house (that is, upstairs by the window) so she immediately believed Tom would be driving that same car back home again.
However, things take a turn and Daisy drives Gatsby's car back home after leaving the hotel in which an argument took place. Gatsby is presumably in the passenger seat. Myrtle sees this car approaching and she runs towards it. It is then that she is killed. Wilson assumed Tom was driving the car and so he visited Tom on the day Gatsby died. Tom then managed to convince Wilson that the man who killed his wife was in fact Gatsby and he, presumably, directed Wilson to Gatsby's abode where he then avenges Myrtle's death.