"When filing Form 709, do I actually compute a tax amount on line 4 of Part 2-Tax Computation"
Yes, but then you enter the applicable credit (typically $4,417,800) on Line 7 (see instructions at link below).
If you are giving substantial gifts, you really should consider getting professional assistance, both with the amount and method of gifting and the filing of any gift tax returns that may be due.
See https://www.irs.gov/instructions/i709#idm140297521158896
