How to add a condition to a generic case_when statement including the glue function?

I have two data frames (df1 and df2) as you can see in the tables below. Based on the conditions in df1, I need to check the values in df2. The expected output is also presented. The condition is based on the columns dep and value in df1 checked in df2 against the the variables taken from the column var in df1. Please see the following examples:

For instance, based on row 1 in df1, we judge whether the values in column A in df2 are TRUE or FALSE.

1. if E == 1, A == TRUE

2. if E != 1, we need to check the following conditions:

   - if A == NA, A == TRUE

   - if A == any values other than NA, A == FALSE

3. If A and E are both NAs, A == TRUE

Here is the code that works for the first two conditions, my question is how to add the third condition:

library(tidyverse)
library(rlang)
library(glue)
rules_1 <- tibble::tribble(
  ~var, ~value,    ~dep,
  "A",   "==1",    "E", 
  "B",   "==1",    "E", 
  "C",   "!=0",    "A", 
  "D",   "==2",    "G", 
  "E",      NA,     NA, 
  "F",      NA,     NA, 
  "G",    "%in% c('b','d')",     "F",
)

df2 <- data.frame(
  stringsAsFactors = FALSE,
  ID = c("1q", "2d", "4f", "3g", "8j", "5g", "9l"),
  B = c(1L, 1L, NA, 1L, 2L, NA, 1L),
  G = c(3L, 3L, NA, 2L, 2L, NA, NA),
  A = c(0L, 0L, 1L, 1L, 1L, NA, NA),
  C = c(NA, 1L, 1L, NA, NA, 1L, 1L),
  D = c(NA, 1L, 1L, 1L, 1L, 3L, 2L),
  E = c(2L, 2L, 1L, NA, NA, 3L, 1L),
  F = letters[1:7]
)

# And for variables that have NA values in df1, we do not need to do anything. 

(rules_2 <- filter(rules_1,
                   !is.na(dep)))

# rules from data
(rules_3 <- mutate(rules_2,
                   rule = glue("case_when({dep}{value}~TRUE,is.na({var})~TRUE,TRUE ~ FALSE)")))

(mutators <- rules_3$rule)
names(mutators) <- rules_3$var

(parsed_mutators <- rlang::parse_exprs(mutators))

mutate(df2,
       !!!parsed_mutators) 

extend the case_when logic

case_when( {dep}{value}~TRUE,
           is.na({dep}) & is.na({var}) ~ TRUE,
           is.na({var})~TRUE,
           TRUE ~ FALSE)