Not following instructions
As found by Pieter Geerkens, the instructions for the 1860 census repeatedly state that values should be written in dollars only. However, from context, we can quickly rule out $12 and $10 as plausible values for these columns, so the logical conclusion is that the clerk failed to obey that instruction for these values, and wrote the prices in terms that he was familiar with in every day life.
The symbol
I believe the symbol shown is the "solidus", a symbol for the shilling which evolved over time from a "long s" to an oblique or slash.
In the pre-decimal currency of pounds, shillings, and pence, used in the UK until 1972, it was common to write prices with shillings and pence divided with this mark, so that "2/6" meant "2 shillings and 6 pence". In this notation, two shillings exactly would be written "2/-". Written in cursive script, this would look exactly as shown in your image, with a tall oblique, and the "/-" joined up to the preceding number.
This would make the values "12 shillings" and "10 shillings", respectively. But whose "shilling", and what was it worth in US dollars?
The circulation of multiple currencies
In 1857 an Act was passed in the US Congress officially revoking the legal tender status of foreign coins, which up until then had been encouraged because not enough locally minted coins were available.
These weren't going to disappear overnight, so we can assume that in 1860 many people were still accustomed to them in every day life. This would also make sense of the reminders in the census instructions to write values in dollars - today, it would mostly go without saying, since the US Dollar is firmly established as the local currency.
The British shilling - a red herring
The most obvious shilling to look at is the British one - worth twelve pence, and one-twentieth of a pound sterling. According to this Encyclopedia Britannica article, the values of the two currencies on the gold standard valued 1 British pound at 4.8665 U.S. dollars (113.00 grains of gold vs 23.22 grains).
A shilling would thus be $4.8665 / 20, which is just over 24 cents. This leads to values of $2.92 and $2.43, which seem suspiciously high given the context provided.
American shillings
The Merriam-Webster entry for "shilling" includes this broad definition:
any of several early American coins
This confirms that the term was in colloquial use, and even in some cases the official name of coins with varying values.
The Spanish "shilling"
The currencies specifically mentioned in the 1857 Act are not British currency, but the Spanish and Mexican dollar. These were the basis of the US dollar, and were widely used at the time. Two noteworthy things can be seen in the Act:
- The Spanish dollar was generally being treated as equivalent in value to the US dollar. The Act makes provision to redeem coins for less than that value after two years have passed, because they wanted to take them out of circulation.
- The conventional fractions of this coin were not based on hundredths like the US Dollar, but halves, quarters, eighths, and sixteenths. (This is the origin of the term "pieces of eight" - a Spanish dollar divided into eight pieces.)
One eighth of a Spanish dollar was called a "real", plural "reales". These appear to have been in common usage at the time, and had various nicknames in different parts of the country (see for instance this article and this quote and discussion). These apparently included "bit", "levy" ... and "shilling".
The possible value
If taken as one-eighth of a US Dollar, a real would be worth 12.5 cents. (Since a British shilling was worth 12 pence, this multiple may explain the colloquial usage.)
If this is indeed the "shilling" meant by the clerk filling in this form, we would have values of $1.50 for "12/-" and $1.25 for "10/-", which are right in the middle of your ranges from other counties.
A caveat
This is definitely not a conclusive answer, and there are other possible interpretations along similar lines: "shilling", or just the shilling symbol, might have colloquially been used for 12 cents (in the same way "penny" colloquially means 1 cent), or a dime (a division between cents and dollars in the same way a shilling was between pence and pounds), or some other obsolete coin in local use.