I am not really sure about this as the historical method only provides information on what evidence should not be used (source criticism).
The short answer is that all the available evidence should be examined when we are attempting to write history.
The question then becomes how do we use those sources.
I'm fairly sure I mentioned this on another answer, but it may be worth repeating.
Many years ago*, when I was studying the subject, my tutor suggested seven guidelines to help us evaluate the relative 'value' of historical sources:
- If all the sources agree about an event, we can consider the event proved.
- However, majority rule does not apply; Even if a majority of sources relate events in one way, that version will not be accepted unless it can pass the test of critical textual analysis.
- In general, a source where part of the account can be confirmed by referring to independent authorities, can probably be trusted in its entirety – even if it is impossible to similarly confirm the whole text.
- When two sources disagree on a particular point, we generally prefer the source with the most "authority". This will be the source created closest in time to the event in question, by a person with particular expertise, or by an eyewitness.
- In general, eyewitnesses are preferred, particularly when they are dealing with events known by most, or at least many, contemporaries.
- If two or more independently created sources agree on a matter, the reliability of each is reinforced.
- When multiple sources disagree, and we have no other means of evaluation which source is "best", then Occam's Razor applies. Good historians choose the source which seems to accord best with common sense.
(Ironically, she never quoted her source for these guidelines!).
Now, obviously, several of these guidelines are highly subjective - especially the last one! It is thus not surprising that interpretations of events based on the same evidence will often vary depending on the personal views or prejudices of particular historians.
*Almost so long ago that Pontius was still in training for his Pilate's licence, and Centurion was a rank and not a tank!
Every historical essay has a different topic of inquiry and so will have a different legitimate source basis. Within this, however, an essay into a topic must be capable of supporting its claims with sources adequate for the scope of the claims and adequate to have had discovered refutation of the claims.
Usually this means the major archival holdings for agencies, or the appropriate archival topical search for claims not focused on an agent.
On top of this the essay must demonstrate its theoretical tools or concepts are not perverse, and assay the appropriate historiography and other fields' secondary literature.
In some areas particular kind as of primary source or their uses are considered perverse for certain claims based on source criticism. Repeated passing of laws, for example, generally means the law failed to regulate a social conduct.
The general process for agreement then is to publish and potentially be damned.