This is mostly hypothetical, as my sister and I plan to sell the rental property we inherited from our father as soon as the current tenant dies (any day now). But if we didn’t see eye to eye and one of us wanted to sell and the other wanted to put it back on the rental market, and we couldn’t come to an agreement, what happens? Does one party sue the other to buy him/her out and proceed without the other? Does the age of the siblings come into play (like, the oldest gets to cast the tiebreaking vote)?
All parties must agree or they have to buy each other out for the fair market value of their share. The process will vary by state and may require an independent arbitrator to become involved, again depending on you local laws.
Age of the siblings is moot, generally only the oldest tries to play that card. It means nothing except in the context of nobility and royal families. I’m assuming that you are not the Earl of Homie. 
If only.
If the property owners can’t come to an agreement, the courts can order a “partition,” which compels the owners to sell the property and divide the proceeds.
You go to court to force a partition sale, which will cost both of you a very significant amount of money to the point its is highly encouraged you solve this person to person. Forcing a partition sale through the courts is basically mutually assured destruction.
This thread reminds me of my friend who has spent his last five years doing little else than try to settle his father-in-law’s estate that he is the executor. The problem is his sister-in-law who lived rent-free and income-free with the father and feels she has inherited the right to go on doing so. Other heirs disagree and want to sell the property and divide the proceeds. As I said, this fight has been going on for five years and they don’t want to go to court.
Sister and you both own an equal amount. You buy her half or she buys yours. Whatever the future of the property is (rental, sale, destruction) matters not at all. Do you want to keep it? Does she want it? Kind of like a divorce, if you cannot agree, you probably end up selling it and splitting the money. Or you both could let legal fees eat up the equity value of the home until you both walk awary with very little.
This is the only part of the OP that matters. If you cannot agree on a disposition, one party sues the other for a partition sale. Short of that, you’ve agreed to something, even if it’s not what you (or the other party) really want. Rock/paper/scissors, steel deathcage match, one buys the other out at any agreed price (could be based on FMV, could include a kicker as an inducement, or a reduction for any number of reasons), even waiting until the other person dies: all are some form of an agreement, or at least a settlement.
I recall a property me and the sibs inherited from our parents, and question of % ownership was attempted to be debated. One sibling claimed that the % should be split according to the number of grandchildren rather than the number of children our parents had. Guess who had generated the most grandchildren and guess who didn’t generate any.