Do we have any sources addressing which of Moshe Rabbeinu's older siblings, Miriam and Aaron, was older?
דלא היה אהרן בכור דמרים גדולה ממנו ג' שנים כדאמר במדרש [ריש פ' שמות] כמו שהיה אהרן גדול ממשה ג' שנים
Aharon was not the firstborn, because Miriam was three years older than him, as the Midrash states, just like Aharon was three years older than Mosheh.
The Midrash that Tosafot refers to seems to be Shemot Rabbah 1:13:
וְלֹא הָיוּ לְמִרְיָם אֶלָּא חָמֵשׁ שָׁנִים, שֶׁאַהֲרֹן גָּדוֹל מִמּשֶׁה שָׁלשׁ שָׁנִים
Miriam was only five years old [at the time of Pharaoh's decree against the Hebrew boys] as Aharon was three years older than Mosheh.
Conversely, Ramban to Shemot 15:20:
ואמר אחות אהרן דרך כבוד לו, שהוא אחיה הגדול ואחותו הנביאה מתיחסת אליו
Referring to Miriam as Aharon's sister is a way of honoring him because he is her elder brother, and his sister the prophetess is to be identified through him.
However, as noted by Alex in a comment, it's possible that Ramban does not mean that Aharon was older than Miriam, but just that he was the elder of her two brothers.
See also Rashbam to Shemot 15:20:
אחות אהרן - על שם הבכור קורא אחות
'[Miriam] the sister of Aharon' - the sister is known by the name of the firstborn
which implies that Aharon was older than Miriam.
There's another Ramban which insinuates that Miriam was older than Aaron (shemot 2:1) at the end:
ואע"פ שהיה אהרן קטן, נתן השם שמחה בלבו בענין זה, או מרים מלמדתו.
The Gemara Sota says the 2 children danced at their parents' second wedding, and the Ramban suggests that (the older) Miriam taught Aaron how to rejoice.
Another data point, also showing that Miriam was older:
Shir Hashirim Rabbah 2:11 says that the most intense period of the Jews' enslavement in Egypt began when Miriam was born (a note inserted into the text says that this is why she was named Miriam, related to maror, bitter), and lasted for 86 years.
Shemos 7:7 records that Aharon was 83 years old when he and Moshe confronted Pharaoh, which was shortly before the Exodus.
So at the time of the Exodus, Aharon was 83 or 84 years old, and Miriam was 86 or 87.