Are electors allowed to cast a private/personal vote for candidates of their choice during Election Day on November 08 and then also as an Elector in December?
The answer is that electors in the electoral college are allowed to vote in the general as well as their role as Elector. It's difficult to abridge someone's right to vote in the general election, although it can be done on occasion, such as for felons. Wiki defines the suffrage requirements as:
Eligibility to vote in the United States is established both through the federal constitution and by state law. Several constitutional amendments (the 15th, 19th, and 26th specifically) require that voting rights cannot be abridged on account of race, color, previous condition of servitude, sex, or age for those above 18; the constitution as originally written did not establish any such rights during 1787–1870. In the absence of a specific federal law or constitutional provision, each state is given considerable discretion to establish qualifications for suffrage and candidacy within its own respective jurisdiction; in addition, states and lower level jurisdictions establish election systems, such as at-large or single member district elections for county councils or school boards.
Here you can find a summary of State laws on Electors None have a prohibition against voting in the general election.
The National Archives provides this summary of the qualifications to be an elector. Note that not voting in the general is not one of them.
What are the qualifications to be an Elector? The U.S. Constitution contains very few provisions relating to the qualifications of Electors. Article II, section 1, clause 2 provides that no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector. As a historical matter, the 14th Amendment provides that state officials who have engaged in insurrection or rebellion against the United States or given aid and comfort to its enemies are disqualified from serving as Electors. This prohibition relates to the post-Civil War era.
The National Association of Secretaries of State (NASS) has compiled a brief summary of state laws about the various procedures, which vary from state to state, for selecting slates of potential electors and for conducting the meeting of the electors. The document, Summary: State Laws Regarding Presidential Electors, can be downloaded from the NASS website.
Each state's Certificates of Ascertainment confirms the names of its appointed electors. A state's certification of its electors is generally sufficient to establish the qualifications of electors.