I've read pretty much everywhere that the consensus is that Jesus died between AD 30–33, but I can't seem to find where this conclusion comes from.
Are there some historical sources or pieces of evidence that have suggested this dating? Otherwise, how have scholars arrived at this dating?
It's not exactly clear but that's more or less the range, as u/QuickSpore explains here
John the Baptist begins preaching in the 15th year of emperor Tiberius, then a year or so later baptizes Jesus, then 3 years later Jesus is crucified. That's kind of pierced together from sources (the new testament) that weren't super precise with chronology.
So, you're aware Luke 3 implies a date of 29 CE for the start of Jesus' ministry. The text specifies the date 'Tiberius 15', which in the Syrian calendar translates to the year from October 28 CE to September 29 CE. The question over the death-date is therefore equivalent to a question over the length of Jesus' ministry.
The next thing to be aware of is that no further dating information is given explicitly in the New Testament gospels, so all dates that you see -- in this case, 29 to 33 CE -- are inferences based on this information. Some are ancient inferences, others are modern.
For example, one modern inference could be that the start of John the Baptist's ministry in Luke 3.1-3 is not to be understood as contemporaneous with the start of Jesus' ministry in Luke 3.23. Ancient commentators saw no objection to this, however: when ancient sources talk about Jesus' dates, they assume without question that Luke 3.1-3 and Luke 3.23 refer to the same timeframe.
A common ancient inference was that the Jesus' ministry lasted either three years, or was over within one year. I'll call these the 'long chronology' and 'short chronology' for short. The long chronology was premised on the fact that John mentions three Passovers in the course of Jesus' ministry (including the one at which he died); the short chronology was premised on the fact that the synoptic gospels, especially Luke (since he gives the most chronological info), mention only one.
Like I said, these are ancient inferences. There's all sorts of logical moves you could make to generate other periods of time; Irenaeus, for one, believed that Jesus' ministry lasted nearly two decades. But these are the inferences underlying the chronographic thought which produced the traditional 29-33 CE dates. So the short chronology produced a date of 29 CE (assuming death within one year) or 30 CE (assuming death exactly one year later); the long chronology produced a death date of 31 or 32 CE.
There was a lot of numerological/typological thinking involved as well. For example the Valentinians in the 2nd century believed that Jesus' ministry lasted precisely 12 months to the day, one month for each apostle. That belief didn't win over its competitors, of course. Another typological belief was that there was a close link between Jesus' death and the date of the spring equinox, since (a) Passover is related to the equinox in the Hebrew calendar, and (b) in ancient Judaeo-Christian thought, anniversaries were really important and some people believed that the events of Easter were tied to the precise day of the solstice, which in the Julian calendar was traditionally reckoned as happening on 25 March.
Another factor was days of the week. With the 29 CE death date, there was the advantage that 25 March that year fell on a Friday -- that is, one version of the short chronology puts the crucifixion on Friday 25 March 29 CE. In a similar fashion, one version of the long chronology puts the resurrection on Sunday 25 March 31 CE.
Just for reference, among 2nd-4th century sources we get a 29 CE date for the crucifixion given by Clement of Alexandria, Tertullian, Hippolytus of Rome, and Lactantius; the 29 CE date is rejected by Julius Africanus; we get 31 CE given by Eusebius and Epiphanius. Eusebius gives 30/31 CE, probably as a result of some rather inaccurate efforts to reconcile different calendar systems with one another.
In addition there are some ancient sources who have evidently read material based on both the long and short chronologies, and have got confused by them. So for example Lactantius puts the resurrection on 25 March 29 CE, and the crucifixion on 23 March, evidently unaware that those days were a Friday and a Wednesday respectively. There are two 2nd-4th century sources that specify 25 March and the year 29 CE and the crucifixion: Tertullian and Hippolytus of Rome. The other sources report only some the year, or the day-and-month, or they fail to distinguish different dates for the crucifixion and resurrection.
So, this chunk of ancient chronography is obviously misled, but these are the ancient traditions that we find. That's how we get the 29 CE and 31 CE dates. How do we get from there to 30 and 33 CE?
By now, if you've been following this, there's a seemingly unavoidable answer. If someone believes Jesus was born in 1 BCE (he probably wasn't), and they don't care about ancient typological preoccupations with the equinox, then an age of 30 (short chronology) will produce a death date of 30 CE, and an age of 33 (long chronology) will produce a death date of 33 CE. Now, I don't know the details of how and when modern thought left behind these ancient preoccupations while still keeping the two variant chronologies. It's possible that some other reasoning was used. But, as someone who's done a fair amount of research into what the ancient sources have to say -- and which I've summarised offsite here -- I find it hard to imagine that the modern 30 CE and 33 CE dates were invented on some other basis.