What was the subject of the 1862 tax?

The subject of an excise tax is always an activity or event, avoidable if one wishes to avoid the tax. Working for the United States is certainly avoidable, but we must be careful not to conclude that the subject of the tax is merely the act of working for the government. It is the exercise of privilege that is the subject of the tax:

"PRIVILEGE: A particular benefit or advantage enjoyed by a person, company, or class beyond the common advantages of others citizens. An exceptional or extraordinary power of exemption. A particular right, advantage, exemption, power, franchise, or immunity held by a person or class, not generally possessed by others." Black's Law Dictionary, 6th Ed.

Here are some relevant court decisions that make this clear:

'The terms "excise tax" and "privilege tax" are synonymous. The two are often used interchangeably.' (American Airways v. Wallace 57 F.2d 877, 880)

"An income tax is neither a property tax nor a tax on occupations of common right, but is an EXCISE tax...The legislature may declare as 'privileged' and tax as such for state revenue, those pursuits not matters of common right, but it has no power to declare as a 'privilege' and tax for revenue purposes, occupations that are of common right." (Simms v. Ahrens, 271 SW 720) (1925)

From here on we use the terms "federally privileged" and "federally connected" interchangeably; they refer to the same avoidable and privileged federally-connected activities.

To summarize: the income tax is an excise tax, a tax on the exercise of federal privilege.