How many people did you vote for that weren't Republican or Democrat in your local elections? If you didn't vote for them (3rd party, new party) there, don't expect them to ever exist as a presidential candidate. You can't even qualify to be on the ballot if you don't have the party established. You have to petition on all 50 states to be shown there and you will likely be denied on many.

If you don't like the Republican or Democrat party, a solution would be to get local candidates to run under a new party that fits your views better, still you would NEED to vote for whichever of the 2 parties fits your views best in the presidential vote to SLOW the movement right/left/up/down whatever... And establish that party in enough city's/counties/states to take seats that matter there. Once known... Then and only then would it be viable to split the vote, and you likely lose 4 years to a hard push into the directions you don't want... While the final negotiations and realizations of merging or replacing/allying with the lesser evil party.

Likely meaning a pledge that you would hold primaries that would endorse each other if the winner of a primary shows more people. But you cannot and will not win a presidential election if you split the vote and don't endorse each other

In most other countries your 2 parties would be classified right wing and extreme right wing.