The so-called "two witness" rule is a demonstration of how far lacking in Biblical scholarship and just plain logical thinking the JW religion is.
The rule (Deut. 19.15) uses an idiomatic expression requiring not two but "two witnesses or more." It is often repeated in the New Testament as "two or three witnesses."
This idiom is understood in the Jewish list of 613 Mizvot (Commandments) not as requiring at least two people to witness a crime but instructing Jews "not to decide a case on the evidence of a single witness."--Mizvot 227.
Two points of difference exist in how this is applied by Jews that shows how far off the target the JWs are in trying to apply this command from the Mosaic Law.
This commandment means that no judicial case should be concluded or finalized without thorough investigation. The idiom is neither asking for a literal number of witnesses nor is it speaking about establishing the validity of an accusation. It is about settling a case and requiring that justice be done in the sense that regardless of the charge and the opinion of the majority, no one should be judged adversely without due process and sufficient evidence to support any final decision.
In other words an accusation is not enough to decide a case. There must be evidence to support every conclusion made by judges.
Second, any reference to the application of this commandment in the New Testament is merely referring to the principles involved. The New Testament makes it very clear that Gentile Christians are NOT obligated to observe the Mosaic Law or meet any of its demands as a requisite for salvation.
The Greek text reveals an attempt to keep the Jewish idiom intact, often retaining the "two or three witnesses" expression. Again as this is an idiomatic expression, it is not literal. It is a reminder of not running to quick judgment without sufficient evidence. But one thing it is also not doing is discussing how to judge the validity of an accusation of a victim in a case, though sadly this is how it is often used by JW elders.
It's appearance in 1 Timothy 5.19 is evidence that its application is not meant to be taken at face value by Christians. It is stated in a context of applying lessons from two other commandments from the Mosaic Law, with verse 18 making reference to not muzzling an ox and verse 20 referencing the statement in Deuteronomy that carrying out judgment should be enough to strike fear in the hearts of criminals. All three verses, 18-20, are not enforcing the Mosaic Law upon Christians. Instead they are calling to mind lessons from the Law on carrying out justice. Therefore it is not right to impose and enforce a literal "two witness" rule.